LMFDB - Embedded newform 570.2.bb.a.41.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(41,570)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 13]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("570.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.3
Character	$\chi$	$=$	570.41
Dual form			570.2.bb.a.431.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(-1.64147 - 0.552780i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(-0.902121 - 1.47857i) q^{6} +(-1.68197 - 2.91326i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.38887 + 1.81475i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(-1.64147 - 0.552780i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(-0.902121 - 1.47857i) q^{6} +(-1.68197 - 2.91326i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.38887 + 1.81475i) q^{9} +(0.642788 + 0.766044i) q^{10} +(-3.29728 - 1.90369i) q^{11} +(0.259343 - 1.71252i) q^{12} +(1.25387 - 3.44498i) q^{13} +(0.584142 - 3.31284i) q^{14} +(-1.52055 - 0.829421i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.18678 - 1.41436i) q^{17} +(0.663483 + 2.92571i) q^{18} +(-3.97780 - 1.78244i) q^{19} +1.00000i q^{20} +(1.15052 + 5.71180i) q^{21} +(-1.30220 - 3.57776i) q^{22} +(3.04913 - 0.537643i) q^{23} +(1.29946 - 1.14517i) q^{24} +(0.939693 + 0.342020i) q^{25} +(3.17491 - 1.83304i) q^{26} +(-2.91811 - 4.29938i) q^{27} +(2.57693 - 2.16230i) q^{28} +(5.97496 - 5.01358i) q^{29} +(-0.631665 - 1.61276i) q^{30} +(-1.66831 + 0.963198i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(4.36008 + 4.94753i) q^{33} +(1.81826 - 0.320608i) q^{34} +(-1.15054 - 3.16107i) q^{35} +(-1.37235 + 2.66770i) q^{36} -9.77797i q^{37} +(-1.90144 - 3.92231i) q^{38} +(-3.96251 + 4.96173i) q^{39} +(-0.642788 + 0.766044i) q^{40} +(-5.93136 + 2.15884i) q^{41} +(-2.79012 + 5.11503i) q^{42} +(0.851898 - 4.83136i) q^{43} +(1.30220 - 3.57776i) q^{44} +(2.03745 + 2.20200i) q^{45} +(2.68136 + 1.54808i) q^{46} +(2.47956 + 2.95502i) q^{47} +(1.73154 - 0.0419736i) q^{48} +(-2.15805 + 3.73786i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-2.72990 + 1.66560i) q^{51} +(3.61038 + 0.636607i) q^{52} +(-0.735560 - 4.17157i) q^{53} +(0.528186 - 5.16924i) q^{54} +(-2.91662 - 2.44733i) q^{55} +3.36394 q^{56} +(5.54415 + 5.12468i) q^{57} +7.79975 q^{58} +(1.98629 + 1.66669i) q^{59} +(0.552780 - 1.64147i) q^{60} +(1.66758 + 9.45734i) q^{61} +(-1.89713 - 0.334515i) q^{62} +(1.26882 - 10.0117i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.83304 - 3.17491i) q^{65} +(0.159809 + 6.59263i) q^{66} +(5.36922 + 6.39878i) q^{67} +(1.59895 + 0.923155i) q^{68} +(-5.30226 - 0.802969i) q^{69} +(1.15054 - 3.16107i) q^{70} +(-2.18141 + 12.3714i) q^{71} +(-2.76605 + 1.16145i) q^{72} +(-3.05716 + 1.11271i) q^{73} +(6.28516 - 7.49036i) q^{74} +(-1.35342 - 1.08086i) q^{75} +(1.06463 - 4.22689i) q^{76} +12.8078i q^{77} +(-6.22480 + 1.25385i) q^{78} +(-4.26569 - 11.7199i) q^{79} +(-0.984808 + 0.173648i) q^{80} +(2.41339 + 8.67038i) q^{81} +(-5.93136 - 2.15884i) q^{82} +(-5.22677 + 3.01768i) q^{83} +(-5.42524 + 2.12488i) q^{84} +(1.41436 - 1.18678i) q^{85} +(3.75813 - 3.15344i) q^{86} +(-12.5791 + 4.92683i) q^{87} +(3.29728 - 1.90369i) q^{88} +(-10.7628 - 3.91732i) q^{89} +(0.145358 + 2.99648i) q^{90} +(-12.1451 + 2.14151i) q^{91} +(1.05895 + 2.90944i) q^{92} +(3.27092 - 0.658857i) q^{93} +3.85751i q^{94} +(-3.60785 - 2.44610i) q^{95} +(1.35342 + 1.08086i) q^{96} +(0.624814 - 0.744624i) q^{97} +(-4.05581 + 1.47620i) q^{98} +(-4.42207 - 10.5314i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	−1.64147	−	0.552780i	−0.947705	−	0.319148i
$3$	−1.64147	−	0.552780i	−0.947705	−	0.319148i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.984808	+	0.173648i	0.440419	+	0.0776578i
$5$	0.984808	+	0.173648i	0.440419	+	0.0776578i
$6$	−0.902121	−	1.47857i	−0.368289	−	0.603625i
$7$	−1.68197	−	2.91326i	−0.635725	−	1.10111i	−0.986361	−	0.164597i	$-0.947368\pi$
$7$	−1.68197	−	2.91326i	−0.635725	−	1.10111i	0.350636	−	0.936512i	$-0.385966\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	2.38887	+	1.81475i	0.796290	+	0.604916i
$10$	0.642788	+	0.766044i	0.203267	+	0.242245i
$11$	−3.29728	−	1.90369i	−0.994169	−	0.573983i	−0.0876509	−	0.996151i	$-0.527936\pi$
$11$	−3.29728	−	1.90369i	−0.994169	−	0.573983i	−0.906518	+	0.422168i	$0.861269\pi$
$12$	0.259343	−	1.71252i	0.0748659	−	0.494363i
$13$	1.25387	−	3.44498i	0.347761	−	0.955466i	−0.635313	−	0.772255i	$-0.719129\pi$
$13$	1.25387	−	3.44498i	0.347761	−	0.955466i	0.983074	−	0.183211i	$-0.0586491\pi$
$14$	0.584142	−	3.31284i	0.156119	−	0.885393i
$15$	−1.52055	−	0.829421i	−0.392603	−	0.214156i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	1.18678	−	1.41436i	0.287838	−	0.343032i	−0.602678	−	0.797985i	$-0.705900\pi$
$17$	1.18678	−	1.41436i	0.287838	−	0.343032i	0.890515	+	0.454953i	$0.150344\pi$
$18$	0.663483	+	2.92571i	0.156384	+	0.689597i
$19$	−3.97780	−	1.78244i	−0.912570	−	0.408921i
$19$	−3.97780	−	1.78244i	−0.912570	−	0.408921i
$20$			1.00000i			0.223607i
$21$	1.15052	+	5.71180i	0.251064	+	1.24642i
$22$	−1.30220	−	3.57776i	−0.277630	−	0.762782i
$23$	3.04913	−	0.537643i	0.635787	−	0.112106i	0.153541	−	0.988142i	$-0.450932\pi$
$23$	3.04913	−	0.537643i	0.635787	−	0.112106i	0.482246	+	0.876036i	$0.339821\pi$
$24$	1.29946	−	1.14517i	0.265251	−	0.233756i
$25$	0.939693	+	0.342020i	0.187939	+	0.0684040i
$26$	3.17491	−	1.83304i	0.622651	−	0.359488i
$27$	−2.91811	−	4.29938i	−0.561590	−	0.827416i
$28$	2.57693	−	2.16230i	0.486994	−	0.408636i
$29$	5.97496	−	5.01358i	1.10952	−	0.930999i	0.111493	−	0.993765i	$-0.464437\pi$
$29$	5.97496	−	5.01358i	1.10952	−	0.930999i	0.998028	+	0.0627660i	$0.0199922\pi$
$30$	−0.631665	−	1.61276i	−0.115326	−	0.294449i
$31$	−1.66831	+	0.963198i	−0.299637	+	0.172995i	−0.642280	−	0.766470i	$-0.722011\pi$
$31$	−1.66831	+	0.963198i	−0.299637	+	0.172995i	0.342643	+	0.939466i	$0.388678\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	4.36008	+	4.94753i	0.758993	+	0.861254i
$34$	1.81826	−	0.320608i	0.311829	−	0.0549839i
$35$	−1.15054	−	3.16107i	−0.194476	−	0.534319i
$36$	−1.37235	+	2.66770i	−0.228726	+	0.444617i
$37$		−	9.77797i		−	1.60749i	−0.594975	−	0.803744i	$-0.702838\pi$
$37$		−	9.77797i		−	1.60749i	0.594975	−	0.803744i	$-0.297162\pi$
$38$	−1.90144	−	3.92231i	−0.308454	−	0.636283i
$39$	−3.96251	+	4.96173i	−0.634510	+	0.794513i
$40$	−0.642788	+	0.766044i	−0.101634	+	0.121122i
$41$	−5.93136	+	2.15884i	−0.926323	+	0.337154i	−0.760751	−	0.649044i	$-0.775169\pi$
$41$	−5.93136	+	2.15884i	−0.926323	+	0.337154i	−0.165572	+	0.986198i	$0.552947\pi$
$42$	−2.79012	+	5.11503i	−0.430525	+	0.789266i
$43$	0.851898	−	4.83136i	0.129913	−	0.736775i	−0.848354	−	0.529429i	$-0.822406\pi$
$43$	0.851898	−	4.83136i	0.129913	−	0.736775i	0.978268	−	0.207346i	$-0.0664826\pi$
$44$	1.30220	−	3.57776i	0.196314	−	0.539368i
$45$	2.03745	+	2.20200i	0.303725	+	0.328255i
$46$	2.68136	+	1.54808i	0.395345	+	0.228252i
$47$	2.47956	+	2.95502i	0.361681	+	0.431034i	0.915943	−	0.401307i	$-0.131444\pi$
$47$	2.47956	+	2.95502i	0.361681	+	0.431034i	−0.554263	+	0.832342i	$0.687000\pi$
$48$	1.73154	−	0.0419736i	0.249927	−	0.00605837i
$49$	−2.15805	+	3.73786i	−0.308293	+	0.533980i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−2.72990	+	1.66560i	−0.382263	+	0.233230i
$52$	3.61038	+	0.636607i	0.500669	+	0.0882815i
$53$	−0.735560	−	4.17157i	−0.101037	−	0.573009i	−0.992729	−	0.120367i	$-0.961593\pi$
$53$	−0.735560	−	4.17157i	−0.101037	−	0.573009i	0.891693	−	0.452642i	$-0.149518\pi$
$54$	0.528186	−	5.16924i	0.0718771	−	0.703444i
$55$	−2.91662	−	2.44733i	−0.393277	−	0.329998i
$56$	3.36394			0.449526
$57$	5.54415	+	5.12468i	0.734341	+	0.678781i
$58$	7.79975			1.02416
$59$	1.98629	+	1.66669i	0.258593	+	0.216985i	0.762862	−	0.646562i	$-0.223794\pi$
$59$	1.98629	+	1.66669i	0.258593	+	0.216985i	−0.504269	+	0.863546i	$0.668238\pi$
$60$	0.552780	−	1.64147i	0.0713636	−	0.211913i
$61$	1.66758	+	9.45734i	0.213512	+	1.21089i	0.883470	+	0.468489i	$0.155201\pi$
$61$	1.66758	+	9.45734i	0.213512	+	1.21089i	−0.669957	+	0.742400i	$0.733688\pi$
$62$	−1.89713	−	0.334515i	−0.240936	−	0.0424835i
$63$	1.26882	−	10.0117i	0.159856	−	1.26136i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.83304	−	3.17491i	0.227360	−	0.393799i
$66$	0.159809	+	6.59263i	0.0196712	+	0.811497i
$67$	5.36922	+	6.39878i	0.655954	+	0.781736i	0.986799	−	0.161949i	$-0.0517781\pi$
$67$	5.36922	+	6.39878i	0.655954	+	0.781736i	−0.330845	+	0.943685i	$0.607334\pi$
$68$	1.59895	+	0.923155i	0.193901	+	0.111949i
$69$	−5.30226	−	0.802969i	−0.638317	−	0.0966661i
$70$	1.15054	−	3.16107i	0.137515	−	0.377820i
$71$	−2.18141	+	12.3714i	−0.258885	+	1.46821i	0.527014	+	0.849857i	$0.323312\pi$
$71$	−2.18141	+	12.3714i	−0.258885	+	1.46821i	−0.785899	+	0.618355i	$0.787799\pi$
$72$	−2.76605	+	1.16145i	−0.325982	+	0.136878i
$73$	−3.05716	+	1.11271i	−0.357813	+	0.130233i	−0.514671	−	0.857388i	$-0.672086\pi$
$73$	−3.05716	+	1.11271i	−0.357813	+	0.130233i	0.156858	+	0.987621i	$0.449864\pi$
$74$	6.28516	−	7.49036i	0.730635	−	0.870736i
$75$	−1.35342	−	1.08086i	−0.156279	−	0.124807i
$76$	1.06463	−	4.22689i	0.122121	−	0.484857i
$77$			12.8078i			1.45958i
$78$	−6.22480	+	1.25385i	−0.704820	+	0.141971i
$79$	−4.26569	−	11.7199i	−0.479927	−	1.31859i	−0.909555	−	0.415583i	$-0.863578\pi$
$79$	−4.26569	−	11.7199i	−0.479927	−	1.31859i	0.429628	−	0.903006i	$-0.358645\pi$
$80$	−0.984808	+	0.173648i	−0.110105	+	0.0194145i
$81$	2.41339	+	8.67038i	0.268154	+	0.963376i
$82$	−5.93136	−	2.15884i	−0.655009	−	0.238404i
$83$	−5.22677	+	3.01768i	−0.573713	+	0.331233i	−0.758631	−	0.651521i	$-0.774131\pi$
$83$	−5.22677	+	3.01768i	−0.573713	+	0.331233i	0.184918	+	0.982754i	$0.440798\pi$
$84$	−5.42524	+	2.12488i	−0.591942	+	0.231844i
$85$	1.41436	−	1.18678i	0.153408	−	0.128725i
$86$	3.75813	−	3.15344i	0.405249	−	0.340045i
$87$	−12.5791	+	4.92683i	−1.34863	+	0.528211i
$88$	3.29728	−	1.90369i	0.351492	−	0.202934i
$89$	−10.7628	−	3.91732i	−1.14085	−	0.415236i	−0.298630	−	0.954369i	$-0.596530\pi$
$89$	−10.7628	−	3.91732i	−1.14085	−	0.415236i	−0.842220	+	0.539133i	$0.818752\pi$
$90$	0.145358	+	2.99648i	0.0153221	+	0.315856i
$91$	−12.1451	+	2.14151i	−1.27315	+	0.224491i
$92$	1.05895	+	2.90944i	0.110403	+	0.303330i
$93$	3.27092	−	0.658857i	0.339179	−	0.0683202i
$94$			3.85751i			0.397872i
$95$	−3.60785	−	2.44610i	−0.370158	−	0.250965i
$96$	1.35342	+	1.08086i	0.138133	+	0.110315i
$97$	0.624814	−	0.744624i	0.0634402	−	0.0756051i	−0.733391	−	0.679807i	$-0.762064\pi$
$97$	0.624814	−	0.744624i	0.0634402	−	0.0756051i	0.796831	+	0.604202i	$0.206508\pi$
$98$	−4.05581	+	1.47620i	−0.409699	+	0.149118i
$99$	−4.42207	−	10.5314i	−0.444434	−	1.05845i
$100$	−0.173648	+	0.984808i	−0.0173648	+	0.0984808i
$101$	−1.97235	+	5.41898i	−0.196256	+	0.539209i	−0.998314	−	0.0580366i	$-0.981516\pi$
$101$	−1.97235	+	5.41898i	−0.196256	+	0.539209i	0.802058	+	0.597246i	$0.203738\pi$
$102$	−3.16185	−	0.478828i	−0.313070	−	0.0474110i
$103$	14.7565	+	8.51970i	1.45401	+	0.839471i	0.998705	−	0.0508672i	$-0.0161985\pi$
$103$	14.7565	+	8.51970i	1.45401	+	0.839471i	0.455300	+	0.890338i	$0.349532\pi$
$104$	2.35651	+	2.80837i	0.231074	+	0.275384i
$105$	0.141197	+	5.82481i	0.0137794	+	0.568443i
$106$	2.11796	−	3.66841i	0.205714	−	0.356308i
$107$	6.28886	+	10.8926i	0.607967	+	1.05303i	0.991575	+	0.129533i	$0.0413479\pi$
$107$	6.28886	+	10.8926i	0.607967	+	1.05303i	−0.383608	+	0.923496i	$0.625319\pi$
$108$	3.72734	−	3.62035i	0.358663	−	0.348369i
$109$	8.64590	+	1.52451i	0.828127	+	0.146021i	0.571617	−	0.820520i	$-0.306316\pi$
$109$	8.64590	+	1.52451i	0.828127	+	0.146021i	0.256510	+	0.966542i	$0.417427\pi$
$110$	−0.661144	−	3.74953i	−0.0630376	−	0.357504i
$111$	−5.40507	+	16.0503i	−0.513026	+	1.52342i
$112$	2.57693	+	2.16230i	0.243497	+	0.204318i
$113$	−19.9658			−1.87823			−0.939114	−	0.343606i	$-0.888352\pi$
$113$	−19.9658			−1.87823			−0.939114	+	0.343606i	$0.888352\pi$
$114$	0.952984	+	7.48945i	0.0892551	+	0.701451i
$115$	3.09617			0.288719
$116$	5.97496	+	5.01358i	0.554761	+	0.465500i
$117$	9.24710	−	5.95415i	0.854895	−	0.550461i
$118$	0.450255	+	2.55352i	0.0414493	+	0.235071i
$119$	−6.11652	−	1.07851i	−0.560701	−	0.0988666i
$120$	1.47857	−	0.902121i	0.134975	−	0.0823520i
$121$	1.74806	+	3.02772i	0.158914	+	0.275247i
$122$	−4.80162	+	8.31665i	−0.434718	+	0.752954i
$123$	10.9295	−	0.264938i	0.985483	−	0.0238887i
$124$	−1.23826	−	1.47571i	−0.111199	−	0.132522i
$125$	0.866025	+	0.500000i	0.0774597	+	0.0447214i
$126$	7.40740	−	6.85386i	0.659904	−	0.610590i
$127$	4.34398	−	11.9350i	0.385466	−	1.05906i	−0.583554	−	0.812074i	$-0.698338\pi$
$127$	4.34398	−	11.9350i	0.385466	−	1.05906i	0.969020	−	0.246984i	$-0.0794394\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−4.06905	+	7.45963i	−0.358260	+	0.656784i
$130$	3.44498	−	1.25387i	0.302145	−	0.109972i
$131$	1.44950	−	1.72745i	0.126644	−	0.150928i	−0.698997	−	0.715125i	$-0.746370\pi$
$131$	1.44950	−	1.72745i	0.126644	−	0.150928i	0.825640	+	0.564197i	$0.190814\pi$
$132$	−4.11524	+	5.15297i	−0.358186	+	0.448509i
$133$	1.49782	+	14.5864i	0.129878	+	1.26480i
$134$			8.35302i			0.721591i
$135$	−2.12720	−	4.74078i	−0.183080	−	0.408022i
$136$	0.631475	+	1.73496i	0.0541485	+	0.148772i
$137$	1.56884	−	0.276629i	0.134035	−	0.0236340i	−0.106228	−	0.994342i	$-0.533877\pi$
$137$	1.56884	−	0.276629i	0.134035	−	0.0236340i	0.240263	+	0.970708i	$0.422766\pi$
$138$	−3.54563	−	4.02334i	−0.301824	−	0.342489i
$139$	8.29909	+	3.02062i	0.703919	+	0.256206i	0.669083	−	0.743187i	$-0.266687\pi$
$139$	8.29909	+	3.02062i	0.703919	+	0.256206i	0.0348360	+	0.999393i	$0.488909\pi$
$140$	2.91326	−	1.68197i	0.246215	−	0.142152i
$141$	−2.43665	−	6.22124i	−0.205203	−	0.523923i
$142$	−9.62322	+	8.07484i	−0.807563	+	0.677625i
$143$	−10.6925	+	8.97210i	−0.894155	+	0.750285i
$144$	−2.86548	−	0.888263i	−0.238790	−	0.0740219i
$145$	6.75478	−	3.89988i	0.560954	−	0.323867i
$146$	−3.05716	−	1.11271i	−0.253012	−	0.0920889i
$147$	5.60860	−	4.94266i	0.462589	−	0.407664i
$148$	9.62942	−	1.69793i	0.791533	−	0.139569i
$149$	4.23402	+	11.6329i	0.346864	+	0.953002i	0.983351	+	0.181714i	$0.0581646\pi$
$149$	4.23402	+	11.6329i	0.346864	+	0.953002i	−0.636487	+	0.771287i	$0.719613\pi$
$150$	−0.342015	−	1.69795i	−0.0279254	−	0.138637i
$151$			7.71526i			0.627859i	0.949446	+	0.313929i	$0.101646\pi$
$151$			7.71526i			0.627859i	−0.949446	+	0.313929i	$0.898354\pi$
$152$	3.53254	−	2.55365i	0.286527	−	0.207129i
$153$	5.40177	−	1.22499i	0.436707	−	0.0990349i
$154$	−8.23269	+	9.81134i	−0.663409	+	0.790620i
$155$	−1.81022	+	0.658866i	−0.145400	+	0.0529214i
$156$	−5.57443	−	3.04072i	−0.446312	−	0.243452i
$157$	−1.27647	+	7.23920i	−0.101873	+	0.577751i	0.890550	+	0.454885i	$0.150320\pi$
$157$	−1.27647	+	7.23920i	−0.101873	+	0.577751i	−0.992423	+	0.122866i	$0.960791\pi$
$158$	4.26569	−	11.7199i	0.339360	−	0.932383i
$159$	−1.09856	+	7.25412i	−0.0871212	+	0.575289i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	−6.69484	−	7.97860i	−0.527627	−	0.628802i
$162$	−3.72446	+	8.19319i	−0.292621	+	0.643718i
$163$	10.2297	−	17.7184i	0.801254	−	1.38781i	−0.117537	−	0.993069i	$-0.537500\pi$
$163$	10.2297	−	17.7184i	0.801254	−	1.38781i	0.918791	−	0.394745i	$-0.129167\pi$
$164$	−3.15601	−	5.46637i	−0.246443	−	0.426852i
$165$	3.43471	+	5.62948i	0.267392	+	0.438255i
$166$	−5.94367	−	1.04803i	−0.461318	−	0.0813428i
$167$	−3.12962	−	17.7489i	−0.242177	−	1.37345i	−0.826958	−	0.562263i	$-0.809931\pi$
$167$	−3.12962	−	17.7489i	−0.242177	−	1.37345i	0.584781	−	0.811191i	$-0.301180\pi$
$168$	−5.52182	−	1.85952i	−0.426018	−	0.143465i
$169$	−0.337124	−	0.282881i	−0.0259326	−	0.0217601i
$170$	1.84631			0.141605
$171$	−6.26775	−	11.4767i	−0.479307	−	0.877647i
$172$	4.90589			0.374070
$173$	0.516019	+	0.432992i	0.0392322	+	0.0329197i	0.662193	−	0.749333i	$-0.269626\pi$
$173$	0.516019	+	0.432992i	0.0392322	+	0.0329197i	−0.622961	+	0.782253i	$0.714070\pi$
$174$	−12.8031	−	4.31155i	−0.970599	−	0.326858i
$175$	−0.584142	−	3.31284i	−0.0441570	−	0.250427i
$176$	3.74953	+	0.661144i	0.282632	+	0.0498356i
$177$	−2.33912	−	3.83381i	−0.175819	−	0.288167i
$178$	−5.72674	−	9.91901i	−0.429238	−	0.743461i
$179$	9.20983	−	15.9519i	0.688375	−	1.19230i	−0.283988	−	0.958828i	$-0.591658\pi$
$179$	9.20983	−	15.9519i	0.688375	−	1.19230i	0.972363	−	0.233473i	$-0.0750090\pi$
$180$	−1.81475	+	2.38887i	−0.135263	+	0.178056i
$181$	−14.2567	−	16.9904i	−1.05969	−	1.26289i	−0.963552	−	0.267522i	$-0.913795\pi$
$181$	−14.2567	−	16.9904i	−1.05969	−	1.26289i	−0.0961383	−	0.995368i	$-0.530649\pi$
$182$	−10.6802	−	6.16623i	−0.791670	−	0.457071i
$183$	2.49053	−	16.4458i	0.184106	−	1.21571i
$184$	−1.05895	+	2.90944i	−0.0780669	+	0.214487i
$185$	1.69793	−	9.62942i	0.124834	−	0.707969i
$186$	2.92917	+	1.59779i	0.214778	+	0.117156i
$187$	−6.60566	+	2.40426i	−0.483054	+	0.175817i
$188$	−2.47956	+	2.95502i	−0.180840	+	0.215517i
$189$	−7.61703	+	15.7326i	−0.554057	+	1.14438i
$190$	−1.19145	−	4.19290i	−0.0864368	−	0.304185i
$191$			18.7492i			1.35665i	0.734764	+	0.678323i	$0.237293\pi$
$191$			18.7492i			1.35665i	−0.734764	+	0.678323i	$0.762707\pi$
$192$	0.342015	+	1.69795i	0.0246828	+	0.122539i
$193$	0.301185	+	0.827498i	0.0216797	+	0.0595646i	0.950060	−	0.312066i	$-0.101021\pi$
$193$	0.301185	+	0.827498i	0.0216797	+	0.0595646i	−0.928381	+	0.371631i	$0.878799\pi$
$194$	0.957270	−	0.168793i	0.0687280	−	0.0121186i
$195$	−4.76391	+	4.19827i	−0.341150	+	0.300644i
$196$	−4.05581	−	1.47620i	−0.289701	−	0.105443i
$197$	7.63469	−	4.40789i	0.543949	−	0.314049i	−0.202729	−	0.979235i	$-0.564981\pi$
$197$	7.63469	−	4.40789i	0.543949	−	0.314049i	0.746678	+	0.665186i	$0.231648\pi$
$198$	3.38195	−	10.9100i	0.240345	−	0.775338i
$199$	17.4686	−	14.6579i	1.23831	−	1.03907i	0.240659	−	0.970610i	$-0.422637\pi$
$199$	17.4686	−	14.6579i	1.23831	−	1.03907i	0.997654	−	0.0684580i	$-0.0218079\pi$
$200$	−0.766044	+	0.642788i	−0.0541675	+	0.0454519i
$201$	−5.27631	−	13.4714i	−0.372162	−	0.950201i
$202$	−4.99416	+	2.88338i	−0.351388	+	0.202874i
$203$	−24.6556	−	8.97389i	−1.73048	−	0.629844i
$204$	−2.11433	−	2.39920i	−0.148033	−	0.167978i
$205$	−6.21613	+	1.09607i	−0.434153	+	0.0765530i
$206$	5.82782	+	16.0118i	0.406043	+	1.11559i
$207$	8.25965	+	4.24904i	0.574085	+	0.295328i
$208$			3.66607i			0.254196i
$209$	9.72272	+	13.4497i	0.672534	+	0.930336i
$210$	−3.63595	+	4.55282i	−0.250904	+	0.314174i
$211$	13.7838	−	16.4269i	0.948914	−	1.13087i	−0.0423659	−	0.999102i	$-0.513490\pi$
$211$	13.7838	−	16.4269i	0.948914	−	1.13087i	0.991280	−	0.131770i	$-0.0420660\pi$
$212$	3.98046	−	1.44877i	0.273379	−	0.0995019i
$213$	10.4194	−	19.1014i	0.713923	−	1.30881i
$214$	−2.18410	+	12.3866i	−0.149302	+	0.846733i
$215$	1.67791	−	4.61003i	0.114433	−	0.314401i
$216$	5.18242	−	0.377467i	0.352619	−	0.0256834i
$217$	5.61209	+	3.24014i	0.380974	+	0.219955i
$218$	5.64321	+	6.72532i	0.382207	+	0.455496i
$219$	5.63333	−	0.136555i	0.380665	−	0.00922755i
$220$	1.90369	−	3.29728i	0.128347	−	0.222303i
$221$	−3.38435	−	5.86187i	−0.227656	−	0.394312i
$222$	−14.4574	+	8.82091i	−0.970320	+	0.592021i
$223$	−9.07189	−	1.59962i	−0.607499	−	0.107118i	−0.138567	−	0.990353i	$-0.544250\pi$
$223$	−9.07189	−	1.59962i	−0.607499	−	0.107118i	−0.468932	+	0.883235i	$0.655361\pi$
$224$	0.584142	+	3.31284i	0.0390297	+	0.221348i
$225$	1.62412	+	2.52235i	0.108275	+	0.168156i
$226$	−15.2947	−	12.8338i	−1.01739	−	0.853691i
$227$	−3.59407			−0.238547			−0.119273	−	0.992861i	$-0.538056\pi$
$227$	−3.59407			−0.238547			−0.119273	+	0.992861i	$0.538056\pi$
$228$	−4.08410	+	6.34982i	−0.270476	+	0.420527i
$229$	10.6575			0.704265			0.352133	−	0.935950i	$-0.385457\pi$
$229$	10.6575			0.704265			0.352133	+	0.935950i	$0.385457\pi$
$230$	2.37180	+	1.99018i	0.156392	+	0.131228i
$231$	7.07989	−	21.0236i	0.465823	−	1.38325i
$232$	1.35441	+	7.68126i	0.0889216	+	0.504299i
$233$	23.2545	+	4.10040i	1.52345	+	0.268626i	0.871789	−	0.489881i	$-0.162960\pi$
$233$	23.2545	+	4.10040i	1.52345	+	0.268626i	0.651665	+	0.758507i	$0.274071\pi$
$234$	10.9109	+	1.38278i	0.713271	+	0.0903951i
$235$	1.92875	+	3.34070i	0.125818	+	0.217923i
$236$	−1.29646	+	2.24553i	−0.0843922	+	0.146172i
$237$	0.523496	+	21.5958i	0.0340047	+	1.40280i
$238$	−3.99228	−	4.75781i	−0.258781	−	0.308403i
$239$	15.7324	+	9.08311i	1.01765	+	0.587538i	0.913421	−	0.407016i	$-0.133431\pi$
$239$	15.7324	+	9.08311i	1.01765	+	0.587538i	0.104224	+	0.994554i	$0.466764\pi$
$240$	1.71252	+	0.259343i	0.110543	+	0.0167405i
$241$	−8.36292	+	22.9769i	−0.538703	+	1.48007i	0.309758	+	0.950816i	$0.399752\pi$
$241$	−8.36292	+	22.9769i	−0.538703	+	1.48007i	−0.848461	+	0.529259i	$0.822470\pi$
$242$	−0.607093	+	3.44300i	−0.0390254	+	0.221324i
$243$	0.831307	−	15.5663i	0.0533284	−	0.998577i
$244$	−9.02409	+	3.28450i	−0.577708	+	0.210269i
$245$	−2.77434	+	3.30633i	−0.177246	+	0.211234i
$246$	8.54281	+	6.82242i	0.544670	+	0.434981i
$247$	−11.1281	+	11.4685i	−0.708066	+	0.729723i
$248$		−	1.92640i		−	0.122326i
$249$	10.2477	−	2.06418i	0.649423	−	0.130812i
$250$	0.342020	+	0.939693i	0.0216313	+	0.0594314i
$251$	−17.8743	+	3.15173i	−1.12822	+	0.198935i	−0.706446	−	0.707767i	$-0.749703\pi$
$251$	−17.8743	+	3.15173i	−1.12822	+	0.198935i	−0.421772	+	0.906702i	$0.638592\pi$
$252$	10.0800	−	0.488976i	0.634979	−	0.0308026i
$253$	−11.0773	−	4.03182i	−0.696427	−	0.253479i
$254$	10.9993	−	6.35047i	0.690160	−	0.398464i
$255$	−2.97766	+	1.16625i	−0.186468	+	0.0730333i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	5.19505	−	4.35916i	0.324058	−	0.271917i	−0.466216	−	0.884671i	$-0.654383\pi$
$257$	5.19505	−	4.35916i	0.324058	−	0.271917i	0.790274	+	0.612754i	$0.209938\pi$
$258$	−7.91203	+	3.09888i	−0.492581	+	0.192928i
$259$	−28.4858	+	16.4463i	−1.77002	+	1.02192i
$260$	3.44498	+	1.25387i	0.213649	+	0.0777617i
$261$	23.3718	−	1.13376i	1.44668	−	0.0701778i
$262$	2.22077	−	0.391581i	0.137199	−	0.0241920i
$263$	6.44409	+	17.7050i	0.397360	+	1.09174i	0.963565	+	0.267473i	$0.0861885\pi$
$263$	6.44409	+	17.7050i	0.397360	+	1.09174i	−0.566206	+	0.824264i	$0.691589\pi$
$264$	−6.46472	+	1.30218i	−0.397876	+	0.0801436i
$265$		−	4.23592i		−	0.260210i
$266$	−8.22855	+	12.1366i	−0.504525	+	0.744143i
$267$	15.5014	+	12.3796i	0.948668	+	0.757620i
$268$	−5.36922	+	6.39878i	−0.327977	+	0.390868i
$269$	6.69166	−	2.43556i	0.407998	−	0.148499i	−0.129865	−	0.991532i	$-0.541454\pi$
$269$	6.69166	−	2.43556i	0.407998	−	0.148499i	0.537862	+	0.843033i	$0.319232\pi$
$270$	1.41779	−	4.99899i	0.0862840	−	0.304229i
$271$	0.876684	−	4.97192i	0.0532548	−	0.302023i	−0.946533	−	0.322606i	$-0.895441\pi$
$271$	0.876684	−	4.97192i	0.0532548	−	0.302023i	0.999788	+	0.0205831i	$0.00655227\pi$
$272$	−0.631475	+	1.73496i	−0.0382888	+	0.105198i
$273$	21.1196	+	3.19834i	1.27822	+	0.193572i
$274$	1.37962	+	0.796521i	0.0833456	+	0.0481196i
$275$	−2.44733	−	2.91662i	−0.147580	−	0.175879i
$276$	−0.129957	−	5.36114i	−0.00782251	−	0.322703i
$277$	15.0126	−	26.0025i	0.902017	−	1.56234i	0.0771457	−	0.997020i	$-0.475419\pi$
$277$	15.0126	−	26.0025i	0.902017	−	1.56234i	0.824872	−	0.565320i	$-0.191247\pi$
$278$	4.41585	+	7.64848i	0.264845	+	0.458725i
$279$	−5.73333	−	0.726604i	−0.343245	−	0.0435006i
$280$	3.31284	+	0.584142i	0.197980	+	0.0349092i
$281$	−3.94462	−	22.3711i	−0.235317	−	1.33455i	−0.841946	−	0.539562i	$-0.818590\pi$
$281$	−3.94462	−	22.3711i	−0.235317	−	1.33455i	0.606629	−	0.794985i	$-0.292521\pi$
$282$	2.13235	−	6.33200i	0.126980	−	0.377065i
$283$	6.02489	+	5.05548i	0.358142	+	0.300517i	0.804050	−	0.594562i	$-0.202674\pi$
$283$	6.02489	+	5.05548i	0.358142	+	0.300517i	−0.445907	+	0.895079i	$0.647119\pi$
$284$	−12.5622			−0.745431
$285$	4.57003	+	6.00956i	0.270705	+	0.355976i
$286$	−13.9581			−0.825361
$287$	16.2656	+	13.6485i	0.960130	+	0.805645i
$288$	−1.62412	−	2.52235i	−0.0957023	−	0.148631i
$289$	2.36008	+	13.3847i	0.138828	+	0.787333i
$290$	7.68126	+	1.35441i	0.451059	+	0.0795339i
$291$	−1.43723	+	0.876896i	−0.0842518	+	0.0514045i
$292$	−1.62668	−	2.81749i	−0.0951942	−	0.164881i
$293$	14.8077	−	25.6477i	0.865074	−	1.49835i	−0.00189973	−	0.999998i	$-0.500605\pi$
$293$	14.8077	−	25.6477i	0.865074	−	1.49835i	0.866974	−	0.498354i	$-0.166062\pi$
$294$	7.47352	−	0.181163i	0.435865	−	0.0105656i
$295$	1.66669	+	1.98629i	0.0970386	+	0.115646i
$296$	8.46797	+	4.88898i	0.492191	+	0.284166i
$297$	1.43716	+	19.7314i	0.0833923	+	1.14493i
$298$	−4.23402	+	11.6329i	−0.245270	+	0.673874i
$299$	1.97104	−	11.1783i	0.113988	−	0.646459i
$300$	0.829421	−	1.52055i	0.0478866	−	0.0877888i
$301$	−15.5079	+	5.64440i	−0.893858	+	0.325338i
$302$	−4.95927	+	5.91023i	−0.285374	+	0.340096i
$303$	6.23306	−	7.80484i	0.358080	−	0.448376i
$304$	4.34754	+	0.314462i	0.249349	+	0.0180357i
$305$			9.60323i			0.549880i
$306$	4.92541	+	2.53379i	0.281567	+	0.144847i
$307$	−6.55070	−	17.9979i	−0.373868	−	1.02720i	−0.973852	−	0.227183i	$-0.927049\pi$
$307$	−6.55070	−	17.9979i	−0.373868	−	1.02720i	0.599984	−	0.800012i	$-0.295174\pi$
$308$	−12.6132	+	2.22405i	−0.718704	+	0.126727i
$309$	−19.5130	−	22.1420i	−1.11005	−	1.25961i
$310$	−1.81022	−	0.658866i	−0.102814	−	0.0374211i
$311$	19.4306	−	11.2183i	1.10181	−	0.636130i	0.165114	−	0.986275i	$-0.447201\pi$
$311$	19.4306	−	11.2183i	1.10181	−	0.636130i	0.936696	+	0.350145i	$0.113868\pi$
$312$	−2.31573	−	5.91250i	−0.131102	−	0.334729i
$313$	−6.41396	+	5.38195i	−0.362539	+	0.304206i	−0.805802	−	0.592186i	$-0.798265\pi$
$313$	−6.41396	+	5.38195i	−0.362539	+	0.304206i	0.443263	+	0.896392i	$0.353821\pi$
$314$	−5.63110	+	4.72505i	−0.317781	+	0.266650i
$315$	2.98807	−	9.63932i	0.168358	−	0.543114i
$316$	10.8011	−	6.23602i	0.607609	−	0.350803i
$317$	−29.2358	−	10.6410i	−1.64205	−	0.597656i	−0.654652	−	0.755931i	$-0.727185\pi$
$317$	−29.2358	−	10.6410i	−1.64205	−	0.597656i	−0.987395	+	0.158274i	$0.949407\pi$
$318$	−5.50440	+	4.85084i	−0.308671	+	0.272021i
$319$	−29.2454	+	5.15676i	−1.63743	+	0.288723i
$320$	−0.342020	−	0.939693i	−0.0191195	−	0.0525304i
$321$	−4.30177	−	21.3563i	−0.240101	−	1.19199i
$322$		−	10.4153i		−	0.580423i
$323$	−7.24180	+	3.51064i	−0.402945	+	0.195337i
$324$	−8.11958	+	3.88232i	−0.451088	+	0.215684i
$325$	2.35651	−	2.80837i	0.130715	−	0.155781i
$326$	19.2256	−	6.99755i	1.06481	−	0.387558i
$327$	−13.3493	−	7.28172i	−0.738218	−	0.402680i
$328$	1.09607	−	6.21613i	0.0605204	−	0.343228i
$329$	4.43820	−	12.1939i	0.244686	−	0.672269i
$330$	−0.987417	+	6.52023i	−0.0543555	+	0.358927i
$331$	29.8492	+	17.2335i	1.64066	+	0.947237i	0.980598	+	0.196028i	$0.0628042\pi$
$331$	29.8492	+	17.2335i	1.64066	+	0.947237i	0.660064	+	0.751209i	$0.270529\pi$
$332$	−3.87945	−	4.62335i	−0.212913	−	0.253739i
$333$	17.7445	−	23.3583i	0.972395	−	1.28003i
$334$	9.01137	−	15.6082i	0.493080	−	0.854040i
$335$	4.17651	+	7.23393i	0.228187	+	0.395232i
$336$	−3.03468	−	4.97383i	−0.165556	−	0.271345i
$337$	−8.67182	−	1.52908i	−0.472384	−	0.0832941i	−0.0676121	−	0.997712i	$-0.521538\pi$
$337$	−8.67182	−	1.52908i	−0.472384	−	0.0832941i	−0.404772	+	0.914418i	$0.632649\pi$
$338$	−0.0764199	−	0.433399i	−0.00415669	−	0.0235738i
$339$	32.7734	+	11.0367i	1.78001	+	0.599432i
$340$	1.41436	+	1.18678i	0.0767042	+	0.0643624i
$341$	7.33451			0.397186
$342$	2.57572	−	12.8205i	0.139279	−	0.693254i
$343$	−9.02846			−0.487491
$344$	3.75813	+	3.15344i	0.202625	+	0.170022i
$345$	−5.08227	−	1.71150i	−0.273620	−	0.0921440i
$346$	0.116972	+	0.663381i	0.00628846	+	0.0356636i
$347$	8.24453	+	1.45373i	0.442589	+	0.0780405i	0.390502	−	0.920602i	$-0.372301\pi$
$347$	8.24453	+	1.45373i	0.442589	+	0.0780405i	0.0520874	+	0.998643i	$0.483413\pi$
$348$	−7.03632	−	11.5325i	−0.377186	−	0.618207i
$349$	5.71952	+	9.90650i	0.306159	+	0.530283i	0.977519	−	0.210849i	$-0.0676228\pi$
$349$	5.71952	+	9.90650i	0.306159	+	0.530283i	−0.671360	+	0.741132i	$0.734289\pi$
$350$	1.68197	−	2.91326i	0.0899051	−	0.155720i
$351$	−18.4702	+	4.66196i	−0.985866	+	0.248837i
$352$	2.44733	+	2.91662i	0.130443	+	0.155456i
$353$	20.2613	+	11.6979i	1.07840	+	0.622614i	0.930464	−	0.366383i	$-0.119404\pi$
$353$	20.2613	+	11.6979i	1.07840	+	0.622614i	0.147935	+	0.988997i	$0.452737\pi$
$354$	0.672455	−	4.44043i	0.0357406	−	0.236006i
$355$	−4.29653	+	11.8046i	−0.228036	+	0.626524i
$356$	1.98888	−	11.2795i	0.105410	−	0.597811i
$357$	9.44393	+	5.15143i	0.499826	+	0.272643i
$358$	17.3088	−	6.29989i	0.914799	−	0.332960i
$359$	1.63360	−	1.94685i	0.0862180	−	0.102751i	−0.721211	−	0.692716i	$-0.756414\pi$
$359$	1.63360	−	1.94685i	0.0862180	−	0.102751i	0.807429	+	0.589965i	$0.200859\pi$
$360$	−2.92571	+	0.663483i	−0.154199	+	0.0349686i
$361$	12.6458	+	14.1804i	0.665568	+	0.746338i
$362$		−	22.1794i		−	1.16573i
$363$	−1.19572	−	5.93621i	−0.0627592	−	0.311570i
$364$	−4.21795	−	11.5887i	−0.221081	−	0.607414i
$365$	−3.20393	+	0.564940i	−0.167702	+	0.0295703i
$366$	12.4790	−	10.9973i	0.652288	−	0.574839i
$367$	−21.5764	−	7.85318i	−1.12628	−	0.409932i	−0.289340	−	0.957226i	$-0.593436\pi$
$367$	−21.5764	−	7.85318i	−1.12628	−	0.409932i	−0.836940	+	0.547294i	$0.815658\pi$
$368$	−2.68136	+	1.54808i	−0.139775	+	0.0806994i
$369$	−18.0870	−	5.60674i	−0.941571	−	0.291875i
$370$	7.49036	−	6.28516i	0.389405	−	0.326750i
$371$	−10.9157	+	9.15933i	−0.566713	+	0.475529i
$372$	1.21684	+	3.10682i	0.0630900	+	0.161081i
$373$	−16.9120	+	9.76417i	−0.875672	+	0.505570i	−0.869229	−	0.494410i	$-0.835384\pi$
$373$	−16.9120	+	9.76417i	−0.875672	+	0.505570i	−0.00644319	+	0.999979i	$0.502051\pi$
$374$	−6.60566	−	2.40426i	−0.341570	−	0.124321i
$375$	−1.14517	−	1.29946i	−0.0591362	−	0.0671037i
$376$	−3.79890	+	0.669849i	−0.195914	+	0.0345448i
$377$	−9.77988	−	26.8700i	−0.503689	−	1.38388i
$378$	−15.9477	+	7.15576i	−0.820262	+	0.368053i
$379$			12.0844i			0.620733i	0.950617	+	0.310366i	$0.100452\pi$
$379$			12.0844i			0.620733i	−0.950617	+	0.310366i	$0.899548\pi$
$380$	1.78244	−	3.97780i	0.0914375	−	0.204057i
$381$	−13.7279	+	17.1897i	−0.703304	+	0.880654i
$382$	−12.0518	+	14.3627i	−0.616622	+	0.734862i
$383$	−32.8006	+	11.9384i	−1.67603	+	0.610026i	−0.992758	−	0.120134i	$-0.961667\pi$
$383$	−32.8006	+	11.9384i	−1.67603	+	0.610026i	−0.683276	+	0.730161i	$0.739445\pi$
$384$	−0.829421	+	1.52055i	−0.0423262	+	0.0775951i
$385$	−2.22405	+	12.6132i	−0.113348	+	0.642829i
$386$	−0.301185	+	0.827498i	−0.0153299	+	0.0421185i
$387$	10.8028	−	9.99550i	0.549135	−	0.508100i
$388$	0.841809	+	0.486019i	0.0427364	+	0.0246739i
$389$	4.98873	+	5.94533i	0.252938	+	0.301440i	0.877540	−	0.479503i	$-0.159183\pi$
$389$	4.98873	+	5.94533i	0.252938	+	0.301440i	−0.624602	+	0.780943i	$0.714739\pi$
$390$	−6.34796	+	0.153878i	−0.321441	+	0.00779193i
$391$	2.85824	−	4.95062i	0.144547	−	0.250363i
$392$	−2.15805	−	3.73786i	−0.108998	−	0.188790i
$393$	−3.33422	+	2.03431i	−0.168189	+	0.102617i
$394$	8.68185	+	1.53084i	0.437385	+	0.0771228i
$395$	−2.16575	−	12.2826i	−0.108970	−	0.618002i
$396$	9.60352	−	6.18364i	0.482595	−	0.310740i
$397$	17.6071	+	14.7741i	0.883675	+	0.741491i	0.966931	−	0.255037i	$-0.0820876\pi$
$397$	17.6071	+	14.7741i	0.883675	+	0.741491i	−0.0832564	+	0.996528i	$0.526532\pi$
$398$	22.8036			1.14304
$399$	5.60443	−	24.7711i	0.280572	−	1.24011i
$400$	−1.00000			−0.0500000
$401$	−10.7756	−	9.04181i	−0.538108	−	0.451526i	0.332782	−	0.943004i	$-0.392013\pi$
$401$	−10.7756	−	9.04181i	−0.538108	−	0.451526i	−0.870890	+	0.491477i	$0.836457\pi$
$402$	4.61738	−	13.7113i	0.230294	−	0.683855i
$403$	1.22636	+	6.95502i	0.0610892	+	0.346454i
$404$	−5.67915	−	1.00139i	−0.282548	−	0.0498209i
$405$	0.871125	+	8.95774i	0.0432865	+	0.445114i
$406$	−13.1190	−	22.7227i	−0.651083	−	1.12771i
$407$	−18.6142	+	32.2407i	−0.922672	+	1.59811i
$408$	−0.0774963	−	3.19696i	−0.00383664	−	0.158273i
$409$	19.1165	+	22.7822i	0.945250	+	1.12650i	0.991827	+	0.127590i	$0.0407242\pi$
$409$	19.1165	+	22.7822i	0.945250	+	1.12650i	−0.0465771	+	0.998915i	$0.514831\pi$
$410$	−5.46637	−	3.15601i	−0.269965	−	0.155864i
$411$	−2.72813	−	0.413145i	−0.134569	−	0.0203789i
$412$	−5.82782	+	16.0118i	−0.287116	+	0.788844i
$413$	1.51463	−	8.58990i	0.0745301	−	0.422681i
$414$	3.59603	+	8.56415i	0.176735	+	0.420905i
$415$	−5.67138	+	2.06421i	−0.278397	+	0.101328i
$416$	−2.35651	+	2.80837i	−0.115537	+	0.137692i
$417$	−11.9530	−	9.54584i	−0.585340	−	0.467462i
$418$	−1.19728	+	16.5527i	−0.0585607	+	0.809620i
$419$		−	26.3319i		−	1.28640i	−0.765700	−	0.643198i	$-0.777607\pi$
$419$		−	26.3319i		−	1.28640i	0.765700	−	0.643198i	$-0.222393\pi$
$420$	−5.71180	+	1.15052i	−0.278707	+	0.0561396i
$421$	5.47826	+	15.0514i	0.266994	+	0.733560i	0.998653	+	0.0518890i	$0.0165242\pi$
$421$	5.47826	+	15.0514i	0.266994	+	0.733560i	−0.731659	+	0.681671i	$0.761254\pi$
$422$	21.1180	−	3.72367i	1.02801	−	0.181265i
$423$	0.560720	+	11.5589i	0.0272632	+	0.562015i
$424$	3.98046	+	1.44877i	0.193308	+	0.0703585i
$425$	1.59895	−	0.923155i	0.0775605	−	0.0447796i
$426$	20.2599	−	7.93511i	0.981594	−	0.384457i
$427$	24.7469	−	20.7651i	1.19758	−	1.00489i
$428$	−9.63509	+	8.08480i	−0.465730	+	0.390793i
$429$	22.5111	−	8.81685i	1.08685	−	0.425681i
$430$	4.24862	−	2.45294i	0.204887	−	0.118291i
$431$	11.4535	+	4.16875i	0.551698	+	0.200802i	0.602801	−	0.797892i	$-0.294051\pi$
$431$	11.4535	+	4.16875i	0.551698	+	0.200802i	−0.0511027	+	0.998693i	$0.516274\pi$
$432$	4.21260	+	3.04204i	0.202679	+	0.146360i
$433$	−20.8339	+	3.67357i	−1.00121	+	0.176541i	−0.650145	−	0.759810i	$-0.725292\pi$
$433$	−20.8339	+	3.67357i	−1.00121	+	0.176541i	−0.351066	+	0.936351i	$0.614181\pi$
$434$	2.21639	+	6.08948i	0.106390	+	0.292304i
$435$	−13.2436	+	2.66763i	−0.634981	+	0.127903i
$436$			8.77928i			0.420451i
$437$	−13.0871	−	3.29626i	−0.626043	−	0.157682i
$438$	4.40316	+	3.51643i	0.210391	+	0.168021i
$439$	12.4323	−	14.8162i	0.593361	−	0.707140i	−0.382887	−	0.923795i	$-0.625070\pi$
$439$	12.4323	−	14.8162i	0.593361	−	0.707140i	0.976248	+	0.216655i	$0.0695146\pi$
$440$	3.57776	−	1.30220i	0.170563	−	0.0620799i
$441$	−11.9386	+	5.01293i	−0.568503	+	0.238711i
$442$	1.17537	−	6.66587i	0.0559068	−	0.317063i
$443$	5.75200	−	15.8035i	0.273286	−	0.750846i	−0.724798	−	0.688962i	$-0.758067\pi$
$443$	5.75200	−	15.8035i	0.273286	−	0.750846i	0.998083	−	0.0618843i	$-0.0197110\pi$
$444$	−16.7450	−	2.53585i	−0.794683	−	0.120346i
$445$	−9.91901	−	5.72674i	−0.470206	−	0.271474i
$446$	−5.92126	−	7.05668i	−0.280380	−	0.334144i
$447$	−0.519610	−	21.4355i	−0.0245767	−	1.01387i
$448$	−1.68197	+	2.91326i	−0.0794657	+	0.137639i
$449$	−0.699526	−	1.21162i	−0.0330127	−	0.0571797i	0.849047	−	0.528317i	$-0.177177\pi$
$449$	−0.699526	−	1.21162i	−0.0330127	−	0.0571797i	−0.882060	+	0.471138i	$0.843844\pi$
$450$	−0.377183	+	2.97619i	−0.0177806	+	0.140299i
$451$	23.6671	+	4.17316i	1.11444	+	0.196506i
$452$	−3.46703	−	19.6625i	−0.163075	−	0.924847i
$453$	4.26484	−	12.6644i	0.200380	−	0.595025i
$454$	−2.75322	−	2.31022i	−0.129215	−	0.108424i
$455$	−12.3325			−0.578154
$456$	−7.21018	+	2.23903i	−0.337648	+	0.104852i
$457$	7.33756			0.343237			0.171618	−	0.985164i	$-0.445100\pi$
$457$	7.33756			0.343237			0.171618	+	0.985164i	$0.445100\pi$
$458$	8.16409	+	6.85049i	0.381483	+	0.320102i
$459$	−9.54401	−	0.975195i	−0.445476	−	0.0455182i
$460$	0.537643	+	3.04913i	0.0250678	+	0.142166i
$461$	−33.3356	−	5.87796i	−1.55259	−	0.273764i	−0.669446	−	0.742861i	$-0.733468\pi$
$461$	−33.3356	−	5.87796i	−1.55259	−	0.273764i	−0.883147	+	0.469097i	$0.844579\pi$
$462$	18.9373	−	11.5542i	0.881041	−	0.537549i
$463$	−12.4999	−	21.6505i	−0.580921	−	1.00618i	−0.995371	−	0.0961121i	$-0.969359\pi$
$463$	−12.4999	−	21.6505i	−0.580921	−	1.00618i	0.414450	−	0.910072i	$-0.363974\pi$
$464$	−3.89988	+	6.75478i	−0.181047	+	0.313583i
$465$	3.33564	−	0.0808578i	0.154686	−	0.00374969i
$466$	15.1783	+	18.0888i	0.703121	+	0.837948i
$467$	8.86341	+	5.11729i	0.410150	+	0.236800i	0.690854	−	0.722994i	$-0.257235\pi$
$467$	8.86341	+	5.11729i	0.410150	+	0.236800i	−0.280704	+	0.959794i	$0.590568\pi$
$468$	7.46943	+	8.07269i	0.345275	+	0.373160i
$469$	9.61045	−	26.4045i	0.443769	−	1.21925i
$470$	−0.669849	+	3.79890i	−0.0308978	+	0.175230i
$471$	6.09697	−	11.1773i	0.280933	−	0.515025i
$472$	−2.43654	+	0.886829i	−0.112151	+	0.0408196i
$473$	−12.0063	+	14.3086i	−0.552052	+	0.657910i
$474$	−13.4805	+	16.8799i	−0.619181	+	0.775318i
$475$	−3.12828	−	3.03544i	−0.143535	−	0.139275i
$476$		−	6.21088i		−	0.284675i
$477$	5.81318	−	11.3002i	0.266167	−	0.517400i
$478$	6.21322	+	17.0707i	0.284186	+	0.780794i
$479$	2.52257	−	0.444797i	0.115259	−	0.0203233i	−0.115721	−	0.993282i	$-0.536918\pi$
$479$	2.52257	−	0.444797i	0.115259	−	0.0203233i	0.230980	+	0.972958i	$0.425807\pi$
$480$	1.14517	+	1.29946i	0.0522695	+	0.0593119i
$481$	−33.6849	−	12.2603i	−1.53590	−	0.559022i
$482$	−21.1757	+	12.2258i	−0.964525	+	0.556869i
$483$	6.57899	+	16.7974i	0.299354	+	0.764309i
$484$	−2.67818	+	2.24726i	−0.121735	+	0.102148i
$485$	0.744624	−	0.624814i	0.0338116	−	0.0283713i
$486$	10.6426	−	11.3901i	0.482759	−	0.516666i
$487$	−22.0931	+	12.7554i	−1.00113	+	0.578004i	−0.908583	−	0.417704i	$-0.862835\pi$
$487$	−22.0931	+	12.7554i	−1.00113	+	0.578004i	−0.0925492	+	0.995708i	$0.529502\pi$
$488$	−9.02409	−	3.28450i	−0.408501	−	0.148682i
$489$	−26.5862	+	23.4295i	−1.20227	+	1.05952i
$490$	−4.25053	+	0.749484i	−0.192020	+	0.0338582i
$491$	7.56578	+	20.7868i	0.341439	+	0.938095i	0.984978	+	0.172682i	$0.0552432\pi$
$491$	7.56578	+	20.7868i	0.341439	+	0.938095i	−0.643539	+	0.765413i	$0.722535\pi$
$492$	2.15881	+	10.7175i	0.0973266	+	0.483182i
$493$		−	14.4008i		−	0.648577i
$494$	−15.8964	+	1.63235i	−0.715215	+	0.0734427i
$495$	−2.52613	−	11.1393i	−0.113541	−	0.500674i
$496$	1.23826	−	1.47571i	0.0555997	−	0.0662611i
$497$	39.7101	−	14.4533i	1.78124	−	0.648318i
$498$	9.17704	+	5.00585i	0.411233	+	0.224318i
$499$	−1.69405	+	9.60741i	−0.0758359	+	0.430087i	0.923125	+	0.384501i	$0.125626\pi$
$499$	−1.69405	+	9.60741i	−0.0758359	+	0.430087i	−0.998960	+	0.0455856i	$0.985485\pi$
$500$	−0.342020	+	0.939693i	−0.0152956	+	0.0420243i
$501$	−4.67408	+	30.8644i	−0.208822	+	1.37892i
$502$	−15.7184	−	9.07504i	−0.701548	−	0.405039i
$503$	5.24665	+	6.25272i	0.233937	+	0.278795i	0.870223	−	0.492658i	$-0.163975\pi$
$503$	5.24665	+	6.25272i	0.233937	+	0.278795i	−0.636286	+	0.771453i	$0.719530\pi$
$504$	8.03602	+	6.10470i	0.357953	+	0.271925i
$505$	−2.88338	+	4.99416i	−0.128309	+	0.222237i
$506$	−5.89413	−	10.2089i	−0.262026	−	0.453843i
$507$	0.397010	+	0.650697i	0.0176318	+	0.0288985i
$508$	12.5080	+	2.20549i	0.554952	+	0.0978530i
$509$	−1.84405	−	10.4581i	−0.0817362	−	0.463549i	−0.998013	−	0.0630039i	$-0.979932\pi$
$509$	−1.84405	−	10.4581i	−0.0817362	−	0.463549i	0.916277	−	0.400545i	$-0.131179\pi$
$510$	−3.03067	−	1.02060i	−0.134200	−	0.0451931i
$511$	8.38368	+	7.03474i	0.370872	+	0.311199i
$512$	1.00000			0.0441942
$513$	3.94425	+	22.3034i	0.174143	+	0.984720i
$514$	6.78165			0.299126
$515$	13.0529	+	10.9527i	0.575181	+	0.482634i
$516$	−8.05288	−	2.71188i	−0.354508	−	0.119384i
$517$	−2.55037	−	14.4639i	−0.112165	−	0.636120i
$518$	−32.3928	−	5.71173i	−1.42326	−	0.250959i
$519$	−0.607683	−	0.995989i	−0.0266743	−	0.0437191i
$520$	1.83304	+	3.17491i	0.0803839	+	0.139229i
$521$	−3.81197	+	6.60252i	−0.167005	+	0.289262i	−0.937366	−	0.348347i	$-0.886743\pi$
$521$	−3.81197	+	6.60252i	−0.167005	+	0.289262i	0.770360	+	0.637609i	$0.220076\pi$
$522$	18.6326	+	14.1546i	0.815526	+	0.619529i
$523$	−10.8920	−	12.9806i	−0.476276	−	0.567604i	0.473396	−	0.880850i	$-0.343028\pi$
$523$	−10.8920	−	12.9806i	−0.476276	−	0.567604i	−0.949672	+	0.313246i	$0.898584\pi$
$524$	1.95291	+	1.12751i	0.0853132	+	0.0492556i
$525$	−0.872416	+	5.76083i	−0.0380753	+	0.251423i
$526$	−6.44409	+	17.7050i	−0.280976	+	0.771974i
$527$	−0.617619	+	3.50269i	−0.0269039	+	0.152580i
$528$	−5.78929	−	3.15792i	−0.251947	−	0.137431i
$529$	−12.6048	+	4.58778i	−0.548035	+	0.199469i
$530$	2.72280	−	3.24490i	0.118271	−	0.140950i
$531$	1.72035	+	7.58612i	0.0746570	+	0.329210i
$532$	−14.1047	+	4.00796i	−0.611516	+	0.173767i
$533$			23.1403i			1.00232i
$534$	3.91727	+	19.4474i	0.169517	+	0.841572i
$535$	4.30183	+	11.8192i	0.185984	+	0.510988i
$536$	−8.22612	+	1.45049i	−0.355314	+	0.0626515i
$537$	−23.9356	+	21.0936i	−1.03290	+	0.910256i
$538$	6.69166	+	2.43556i	0.288498	+	0.105005i
$539$	14.2314	−	8.21652i	0.612991	−	0.353911i
$540$	4.29938	−	2.91811i	0.185016	−	0.125575i
$541$	3.44282	−	2.88887i	0.148019	−	0.124202i	−0.565771	−	0.824562i	$-0.691422\pi$
$541$	3.44282	−	2.88887i	0.148019	−	0.124202i	0.713790	+	0.700360i	$0.246977\pi$
$542$	3.86747	−	3.24519i	0.166122	−	0.139393i
$543$	14.0100	+	35.7702i	0.601225	+	1.53504i
$544$	−1.59895	+	0.923155i	−0.0685545	+	0.0395799i
$545$	8.24982	+	3.00269i	0.353384	+	0.128621i
$546$	14.1227	+	16.0255i	0.604397	+	0.685828i
$547$	44.9326	−	7.92283i	1.92118	−	0.338756i	0.922317	−	0.386433i	$-0.126293\pi$
$547$	44.9326	−	7.92283i	1.92118	−	0.338756i	0.998863	+	0.0476771i	$0.0151819\pi$
$548$	0.544853	+	1.49697i	0.0232750	+	0.0639474i
$549$	−13.1790	+	25.6186i	−0.562468	+	1.09337i
$550$		−	3.80738i		−	0.162347i
$551$	−32.7036	+	9.29300i	−1.39322	+	0.395895i
$552$	3.34652	−	4.19041i	0.142437	−	0.178356i
$553$	−26.9683	+	32.1395i	−1.14681	+	1.36671i
$554$	28.2144	−	10.2692i	1.19871	−	0.436296i
$555$	−8.11005	+	14.8679i	−0.344252	+	0.631105i
$556$	−1.53361	+	8.69753i	−0.0650395	+	0.368857i
$557$	−5.59393	+	15.3692i	−0.237023	+	0.651214i	0.762966	+	0.646439i	$0.223742\pi$
$557$	−5.59393	+	15.3692i	−0.237023	+	0.651214i	−0.999989	+	0.00477566i	$0.998480\pi$
$558$	−3.92493	−	4.24192i	−0.166156	−	0.179575i
$559$	−15.5758	−	8.99267i	−0.658784	−	0.380349i
$560$	2.16230	+	2.57693i	0.0913739	+	0.108895i
$561$	12.1720	−	0.295057i	0.513904	−	0.0124573i
$562$	11.3581	−	19.6728i	0.479112	−	0.829847i
$563$	2.06853	+	3.58280i	0.0871783	+	0.150997i	0.906317	−	0.422598i	$-0.138882\pi$
$563$	2.06853	+	3.58280i	0.0871783	+	0.150997i	−0.819139	+	0.573595i	$0.805548\pi$
$564$	5.70361	−	3.47994i	0.240165	−	0.146532i
$565$	−19.6625	−	3.46703i	−0.827208	−	0.145859i
$566$	1.36573	+	7.74545i	0.0574060	+	0.325565i
$567$	21.1998	−	21.6142i	0.890309	−	0.907709i
$568$	−9.62322	−	8.07484i	−0.403781	−	0.338813i
$569$	31.4380			1.31795			0.658975	−	0.752165i	$-0.270990\pi$
$569$	31.4380			1.31795			0.658975	+	0.752165i	$0.270990\pi$
$570$	−0.362023	+	7.54115i	−0.0151635	+	0.315864i
$571$	3.57744			0.149711			0.0748557	−	0.997194i	$-0.476150\pi$
$571$	3.57744			0.149711			0.0748557	+	0.997194i	$0.476150\pi$
$572$	−10.6925	−	8.97210i	−0.447077	−	0.375142i
$573$	10.3642	−	30.7763i	0.432970	−	1.28570i
$574$	3.68712	+	20.9107i	0.153897	+	0.872796i
$575$	3.04913	+	0.537643i	0.127157	+	0.0224213i
$576$	0.377183	−	2.97619i	0.0157160	−	0.124008i
$577$	−4.91134	−	8.50669i	−0.204462	−	0.354138i	0.745499	−	0.666506i	$-0.232211\pi$
$577$	−4.91134	−	8.50669i	−0.204462	−	0.354138i	−0.949961	+	0.312368i	$0.898878\pi$
$578$	−6.79557	+	11.7703i	−0.282658	+	0.489579i
$579$	−0.0369622	−	1.52480i	−0.00153610	−	0.0633687i
$580$	5.01358	+	5.97496i	0.208178	+	0.248097i
$581$	17.5826	+	10.1513i	0.729447	+	0.421147i
$582$	−1.66464	−	0.252091i	−0.0690015	−	0.0104495i
$583$	−5.51601	+	15.1551i	−0.228450	+	0.627661i
$584$	0.564940	−	3.20393i	0.0233774	−	0.132580i
$585$	10.1405	−	4.25795i	0.419260	−	0.176045i
$586$	27.8293	−	10.1291i	1.14962	−	0.418427i
$587$	−18.9904	+	22.6318i	−0.783817	+	0.934116i	−0.999099	−	0.0424354i	$-0.986488\pi$
$587$	−18.9904	+	22.6318i	−0.783817	+	0.934116i	0.215283	+	0.976552i	$0.430933\pi$
$588$	5.84150	+	4.66511i	0.240899	+	0.192386i
$589$	8.35304	−	0.857743i	0.344181	−	0.0353427i
$590$			2.59291i			0.106749i
$591$	−14.9687	+	3.01513i	−0.615732	+	0.124026i
$592$	3.34426	+	9.18828i	0.137448	+	0.377636i
$593$	−13.5183	+	2.38363i	−0.555128	+	0.0978841i	−0.444173	−	0.895941i	$-0.646502\pi$
$593$	−13.5183	+	2.38363i	−0.555128	+	0.0978841i	−0.110956	+	0.993825i	$0.535391\pi$
$594$	−11.5822	+	16.0389i	−0.475223	+	0.658086i
$595$	−5.83632	−	2.12425i	−0.239266	−	0.0870856i
$596$	−10.7209	+	6.18972i	−0.439145	+	0.253541i
$597$	−36.7767	+	14.4042i	−1.50517	+	0.589525i
$598$	8.69519	−	7.29613i	0.355573	−	0.298361i
$599$	6.54295	−	5.49019i	0.267338	−	0.224323i	−0.499257	−	0.866454i	$-0.666394\pi$
$599$	6.54295	−	5.49019i	0.267338	−	0.224323i	0.766595	+	0.642131i	$0.221949\pi$
$600$	1.61276	−	0.631665i	0.0658407	−	0.0257876i
$601$	31.2511	−	18.0428i	1.27476	−	0.735982i	0.298878	−	0.954291i	$-0.403388\pi$
$601$	31.2511	−	18.0428i	1.27476	−	0.735982i	0.975880	+	0.218310i	$0.0700543\pi$
$602$	−15.5079	−	5.64440i	−0.632053	−	0.230049i
$603$	1.21418	+	25.0296i	0.0494452	+	1.01928i
$604$	−7.59804	+	1.33974i	−0.309160	+	0.0545133i
$605$	1.19574	+	3.28527i	0.0486138	+	0.133565i
$606$	9.79166	−	1.97232i	0.397759	−	0.0801200i
$607$			29.6646i			1.20405i	0.798477	+	0.602025i	$0.205639\pi$
$607$			29.6646i			1.20405i	−0.798477	+	0.602025i	$0.794361\pi$
$608$	3.12828	+	3.03544i	0.126868	+	0.123103i
$609$	35.5109	+	28.3595i	1.43897	+	1.14919i
$610$	−6.17284	+	7.35650i	−0.249931	+	0.297856i
$611$	13.2890	−	4.83682i	0.537617	−	0.195677i
$612$	2.14439	+	5.10699i	0.0866819	+	0.206438i
$613$	7.22075	−	40.9509i	0.291643	−	1.65399i	−0.388897	−	0.921281i	$-0.627144\pi$
$613$	7.22075	−	40.9509i	0.291643	−	1.65399i	0.680540	−	0.732711i	$-0.261745\pi$
$614$	6.55070	−	17.9979i	0.264365	−	0.726337i
$615$	10.8095	+	1.63698i	0.435881	+	0.0660094i
$616$	−11.0919	−	6.40390i	−0.446904	−	0.258020i
$617$	17.9675	+	21.4128i	0.723343	+	0.862046i	0.994951	−	0.100362i	$-0.0320000\pi$
$617$	17.9675	+	21.4128i	0.723343	+	0.862046i	−0.271608	+	0.962408i	$0.587556\pi$
$618$	−0.715205	−	29.5044i	−0.0287698	−	1.18684i
$619$	−8.57382	+	14.8503i	−0.344611	+	0.596884i	−0.985283	−	0.170931i	$-0.945322\pi$
$619$	−8.57382	+	14.8503i	−0.344611	+	0.596884i	0.640672	+	0.767815i	$0.278656\pi$
$620$	−0.963198	−	1.66831i	−0.0386830	−	0.0670009i
$621$	−11.2092	−	11.5404i	−0.449810	−	0.463102i
$622$	22.0957	+	3.89606i	0.885956	+	0.156218i
$623$	6.69047	+	37.9435i	0.268048	+	1.52018i
$624$	2.02653	−	6.01776i	0.0811262	−	0.240903i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	−8.37283			−0.334646
$627$	−8.52485	−	27.4519i	−0.340450	−	1.09632i
$628$	−7.35087			−0.293332
$629$	−13.8295	−	11.6043i	−0.551419	−	0.462696i
$630$	8.48502	−	5.46345i	0.338051	−	0.217669i
$631$	3.26435	+	18.5131i	0.129952	+	0.736993i	0.978243	+	0.207463i	$0.0665207\pi$
$631$	3.26435	+	18.5131i	0.129952	+	0.736993i	−0.848291	+	0.529530i	$0.822368\pi$
$632$	12.2826	+	2.16575i	0.488574	+	0.0861487i
$633$	−31.7061	+	19.3449i	−1.26021	+	0.768889i
$634$	−15.5561	−	26.9439i	−0.617810	−	1.07008i
$635$	6.35047	−	10.9993i	0.252011	−	0.436495i
$636$	−7.33467	+	0.177797i	−0.290839	+	0.00705010i
$637$	10.1709	+	12.1212i	0.402987	+	0.480261i
$638$	−25.7180	−	14.8483i	−1.01819	−	0.587850i
$639$	−27.6620	+	25.5949i	−1.09429	+	1.01252i
$640$	0.342020	−	0.939693i	0.0135195	−	0.0371446i
$641$	1.08685	−	6.16381i	0.0429278	−	0.243456i	−0.955792	−	0.294044i	$-0.904999\pi$
$641$	1.08685	−	6.16381i	0.0429278	−	0.243456i	0.998720	+	0.0505886i	$0.0161097\pi$
$642$	10.4322	−	19.1250i	0.411727	−	0.754803i
$643$	−4.49227	+	1.63505i	−0.177158	+	0.0644802i	−0.429076	−	0.903268i	$-0.641161\pi$
$643$	−4.49227	+	1.63505i	−0.177158	+	0.0644802i	0.251918	+	0.967749i	$0.418939\pi$
$644$	6.69484	−	7.97860i	0.263814	−	0.314401i
$645$	−5.30258	+	6.63972i	−0.208789	+	0.261439i
$646$	−7.80414	−	1.96563i	−0.307050	−	0.0773368i
$647$			3.44354i			0.135380i	0.997706	+	0.0676898i	$0.0215628\pi$
$647$			3.44354i			0.135380i	−0.997706	+	0.0676898i	$0.978437\pi$
$648$	−8.71547	−	2.24514i	−0.342376	−	0.0881974i
$649$	−3.37649	−	9.27683i	−0.132539	−	0.364148i
$650$	3.61038	−	0.636607i	0.141611	−	0.0249698i
$651$	−7.42101	−	8.42086i	−0.290852	−	0.330040i
$652$	19.2256	+	6.99755i	0.752933	+	0.274045i
$653$	−1.53537	+	0.886446i	−0.0600837	+	0.0346893i	−0.529741	−	0.848160i	$-0.677711\pi$
$653$	−1.53537	+	0.886446i	−0.0600837	+	0.0346893i	0.469657	+	0.882849i	$0.344378\pi$
$654$	−5.54556	−	14.1589i	−0.216849	−	0.553656i
$655$	1.72745	−	1.44950i	0.0674970	−	0.0566367i
$656$	4.83529	−	4.05729i	0.188786	−	0.158411i
$657$	−9.32244	−	2.88984i	−0.363703	−	0.112743i
$658$	11.2379	−	6.48822i	0.438100	−	0.252937i
$659$	−29.3281	−	10.6746i	−1.14246	−	0.415822i	−0.299660	−	0.954046i	$-0.596873\pi$
$659$	−29.3281	−	10.6746i	−1.14246	−	0.415822i	−0.842802	+	0.538224i	$0.819095\pi$
$660$	−4.94753	+	4.36008i	−0.192582	+	0.169716i
$661$	5.16755	−	0.911179i	0.200994	−	0.0354407i	−0.0722444	−	0.997387i	$-0.523016\pi$
$661$	5.16755	−	0.911179i	0.200994	−	0.0354407i	0.273239	+	0.961946i	$0.411905\pi$
$662$	11.7884	+	32.3883i	0.458169	+	1.25881i
$663$	2.31500	+	11.4929i	0.0899071	+	0.446347i
$664$		−	6.03536i		−	0.234217i
$665$	−1.05783	+	14.6249i	−0.0410210	+	0.567128i
$666$	28.6075	−	6.48751i	1.10852	−	0.251386i
$667$	15.5229	−	18.4995i	0.601048	−	0.716302i
$668$	16.9358	−	6.16414i	0.655267	−	0.238498i
$669$	14.0070	+	7.64050i	0.541543	+	0.295399i
$670$	−1.45049	+	8.22612i	−0.0560372	+	0.317803i
$671$	12.5053	−	34.3581i	0.482763	−	1.32638i
$672$	0.872416	−	5.76083i	0.0336542	−	0.222229i
$673$	−6.42020	−	3.70671i	−0.247481	−	0.142883i	0.371129	−	0.928581i	$-0.378971\pi$
$673$	−6.42020	−	3.70671i	−0.247481	−	0.142883i	−0.618610	+	0.785698i	$0.712304\pi$
$674$	−5.66013	−	6.74548i	−0.218020	−	0.259826i
$675$	−1.27165	−	5.03814i	−0.0489459	−	0.193918i
$676$	0.220042	−	0.381124i	0.00846316	−	0.0146586i
$677$	0.890894	+	1.54307i	0.0342399	+	0.0593052i	0.882638	−	0.470054i	$-0.155766\pi$
$677$	0.890894	+	1.54307i	0.0342399	+	0.0593052i	−0.848398	+	0.529359i	$0.822432\pi$
$678$	18.0116	+	29.5209i	0.691732	+	1.13374i
$679$	−3.22020	−	0.567808i	−0.123580	−	0.0217905i
$680$	0.320608	+	1.81826i	0.0122948	+	0.0697271i
$681$	5.89957	+	1.98673i	0.226072	+	0.0761316i
$682$	5.61856	+	4.71454i	0.215146	+	0.180529i
$683$	−5.86632			−0.224469			−0.112234	−	0.993682i	$-0.535801\pi$
$683$	−5.86632			−0.224469			−0.112234	+	0.993682i	$0.535801\pi$
$684$	10.2140	−	8.16545i	0.390541	−	0.312214i
$685$	1.59304			0.0608670
$686$	−6.91620	−	5.80338i	−0.264062	−	0.221574i
$687$	−17.4939	−	5.89123i	−0.667436	−	0.224765i
$688$	0.851898	+	4.83136i	0.0324783	+	0.184194i
$689$	−15.2933	−	2.69661i	−0.582627	−	0.102733i
$690$	−2.79312	−	4.57791i	−0.106332	−	0.174278i
$691$	14.5856	+	25.2630i	0.554862	+	0.961049i	0.997914	+	0.0645533i	$0.0205623\pi$
$691$	14.5856	+	25.2630i	0.554862	+	0.961049i	−0.443052	+	0.896496i	$0.646104\pi$
$692$	−0.336808	+	0.583368i	−0.0128035	+	0.0221763i
$693$	−23.2429	+	30.5961i	−0.882925	+	1.16225i
$694$	5.38123	+	6.41310i	0.204269	+	0.243438i
$695$	7.64848	+	4.41585i	0.290123	+	0.167503i
$696$	2.02281	−	13.3573i	0.0766745	−	0.506306i
$697$	−3.98589	+	10.9511i	−0.150976	+	0.414804i
$698$	−1.98637	+	11.2653i	−0.0751851	+	0.426396i
$699$	−35.9050	−	19.5853i	−1.35805	−	0.740785i
$700$	3.16107	−	1.15054i	0.119477	−	0.0434862i
$701$	−13.8864	+	16.5492i	−0.524483	+	0.625055i	−0.961635	−	0.274333i	$-0.911543\pi$
$701$	−13.8864	+	16.5492i	−0.524483	+	0.625055i	0.437152	+	0.899388i	$0.355987\pi$
$702$	−17.1456	−	8.30115i	−0.647121	−	0.313307i
$703$	−17.4287	+	38.8948i	−0.657335	+	1.46695i
$704$			3.80738i			0.143496i
$705$	−1.31933	−	6.54985i	−0.0496887	−	0.246682i
$706$	8.00181	+	21.9848i	0.301152	+	0.827408i
$707$	19.1043	−	3.36861i	0.718492	−	0.126690i
$708$	3.36938	−	2.96932i	0.126629	−	0.111594i
$709$	6.62919	+	2.41283i	0.248965	+	0.0906157i	0.463488	−	0.886103i	$-0.346598\pi$
$709$	6.62919	+	2.41283i	0.248965	+	0.0906157i	−0.214524	+	0.976719i	$0.568820\pi$
$710$	−10.8792	+	6.28111i	−0.408289	+	0.235726i
$711$	11.0784	−	35.7384i	0.415474	−	1.34029i
$712$	8.77388	−	7.36216i	0.328815	−	0.275909i
$713$	−4.56903	+	3.83387i	−0.171111	+	0.143580i
$714$	3.92319	+	10.0167i	0.146822	+	0.374864i
$715$	−12.0881	+	6.97906i	−0.452069	+	0.261002i
$716$	17.3088	+	6.29989i	0.646861	+	0.235438i
$717$	−20.8034	−	23.6063i	−0.776916	−	0.881592i
$718$	2.50282	−	0.441314i	0.0934044	−	0.0164697i
$719$	−7.53975	−	20.7153i	−0.281185	−	0.772550i	−0.997222	−	0.0744875i	$-0.976268\pi$
$719$	−7.53975	−	20.7153i	−0.281185	−	0.772550i	0.716037	−	0.698063i	$-0.245954\pi$
$720$	−2.66770	−	1.37235i	−0.0994195	−	0.0511446i
$721$		−	57.3195i		−	2.13469i
$722$	0.572236	+	18.9914i	0.0212964	+	0.706786i
$723$	26.4287	−	33.0932i	0.982894	−	1.23075i
$724$	14.2567	−	16.9904i	0.529845	−	0.631445i
$725$	7.32937	−	2.66767i	0.272206	−	0.0990749i
$726$	2.89975	−	5.31600i	0.107620	−	0.197295i
$727$	−7.69836	+	43.6596i	−0.285517	+	1.61924i	0.417918	+	0.908485i	$0.362760\pi$
$727$	−7.69836	+	43.6596i	−0.285517	+	1.61924i	−0.703435	+	0.710760i	$0.748351\pi$
$728$	4.21795	−	11.5887i	0.156328	−	0.429506i
$729$	−9.96929	+	25.0921i	−0.369233	+	0.929337i
$730$	−2.81749	−	1.62668i	−0.104280	−	0.0602061i
$731$	−5.82223	−	6.93867i	−0.215343	−	0.256636i
$732$	16.6284	−	0.403082i	0.614604	−	0.0148984i
$733$	−24.9320	+	43.1834i	−0.920884	+	1.59502i	−0.122832	+	0.992427i	$0.539198\pi$
$733$	−24.9320	+	43.1834i	−0.920884	+	1.59502i	−0.798051	+	0.602590i	$0.794136\pi$
$734$	−11.4806	−	19.8849i	−0.423756	−	0.733967i
$735$	6.38168	−	3.89365i	0.235392	−	0.143619i
$736$	−3.04913	−	0.537643i	−0.112392	−	0.0198178i
$737$	−5.52255	−	31.3199i	−0.203426	−	1.15368i
$738$	−10.2515	−	15.9211i	−0.377363	−	0.586064i
$739$	−31.7116	−	26.6092i	−1.16653	−	0.978836i	−0.166557	−	0.986032i	$-0.553265\pi$
$739$	−31.7116	−	26.6092i	−1.16653	−	0.978836i	−0.999974	+	0.00719615i	$0.997709\pi$
$740$	9.77797			0.359445
$741$	24.6061	−	12.6738i	0.903927	−	0.465584i
$742$	−14.2494			−0.523112
$743$	15.0997	+	12.6702i	0.553955	+	0.464823i	0.876278	−	0.481807i	$-0.160019\pi$
$743$	15.0997	+	12.6702i	0.553955	+	0.464823i	−0.322323	+	0.946630i	$0.604464\pi$
$744$	−1.06487	+	3.16213i	−0.0390402	+	0.115929i
$745$	2.14967	+	12.1914i	0.0787577	+	0.446657i
$746$	−19.2317	−	3.39106i	−0.704121	−	0.124156i
$747$	−17.9624	−	2.27643i	−0.657210	−	0.0832903i
$748$	−3.51480	−	6.08781i	−0.128514	−	0.222592i
$749$	21.1553	−	36.6421i	0.773000	−	1.33887i
$750$	−0.0419736	−	1.73154i	−0.00153266	−	0.0632270i
$751$	−20.9586	−	24.9775i	−0.764789	−	0.911440i	0.233352	−	0.972392i	$-0.425031\pi$
$751$	−20.9586	−	24.9775i	−0.764789	−	0.911440i	−0.998141	+	0.0609522i	$0.980586\pi$
$752$	−3.34070	−	1.92875i	−0.121823	−	0.0703344i
$753$	31.0825	+	4.70710i	1.13271	+	0.171536i
$754$	9.77988	−	26.8700i	0.356162	−	0.978548i
$755$	−1.33974	+	7.59804i	−0.0487581	+	0.276521i
$756$	−16.8163	−	4.76937i	−0.611603	−	0.173460i
$757$	−5.28078	+	1.92205i	−0.191933	+	0.0698579i	−0.436198	−	0.899850i	$-0.643675\pi$
$757$	−5.28078	+	1.92205i	−0.191933	+	0.0698579i	0.244265	+	0.969708i	$0.421453\pi$
$758$	−7.76769	+	9.25717i	−0.282135	+	0.336235i
$759$	15.9545	+	12.7415i	0.579110	+	0.462486i
$760$	3.92231	−	1.90144i	0.142277	−	0.0689724i
$761$		−	42.3878i		−	1.53656i	−0.640115	−	0.768279i	$-0.721113\pi$
$761$		−	42.3878i		−	1.53656i	0.640115	−	0.768279i	$-0.278887\pi$
$762$	−21.5655	+	4.34391i	−0.781237	+	0.157363i
$763$	−10.1009	−	27.7519i	−0.365676	−	1.00469i
$764$	−18.4644	+	3.25577i	−0.668018	+	0.117790i
$765$	5.53242	−	0.268376i	0.200025	−	0.00970316i
$766$	−32.8006	−	11.9384i	−1.18513	−	0.431354i
$767$	8.23227	−	4.75291i	0.297250	−	0.171617i
$768$	−1.61276	+	0.631665i	−0.0581955	+	0.0227932i
$769$	36.8230	−	30.8981i	1.32787	−	1.11421i	0.343299	−	0.939226i	$-0.388456\pi$
$769$	36.8230	−	30.8981i	1.32787	−	1.11421i	0.984570	−	0.174989i	$-0.0559889\pi$
$770$	−9.81134	+	8.23269i	−0.353576	+	0.296686i
$771$	−10.9372	+	4.28373i	−0.393893	+	0.154275i
$772$	−0.762626	+	0.440303i	−0.0274475	+	0.0158468i
$773$	−3.24561	−	1.18130i	−0.116736	−	0.0424886i	0.282992	−	0.959122i	$-0.408673\pi$
$773$	−3.24561	−	1.18130i	−0.116736	−	0.0424886i	−0.399728	+	0.916634i	$0.630895\pi$
$774$	14.7004	−	0.713111i	0.528394	−	0.0256322i
$775$	−1.89713	+	0.334515i	−0.0681469	+	0.0120161i
$776$	0.332456	+	0.913416i	0.0119345	+	0.0327897i
$777$	55.8498	−	11.2497i	2.00360	−	0.403582i
$778$			7.76108i			0.278248i
$779$	27.4418	+	1.98489i	0.983204	+	0.0711162i
$780$	−4.96173	−	3.96251i	−0.177658	−	0.141881i
$781$	30.7439	−	36.6392i	1.10010	−	1.31105i
$782$	5.37173	−	1.95515i	0.192093	−	0.0699161i
$783$	−38.9909	−	11.0584i	−1.39342	−	0.395196i
$784$	0.749484	−	4.25053i	0.0267673	−	0.151805i
$785$	−2.51415	+	6.90756i	−0.0897338	+	0.246541i
$786$	−3.86179	−	0.584825i	−0.137745	−	0.0208600i
$787$	−10.0308	−	5.79128i	−0.357559	−	0.206437i	0.310451	−	0.950590i	$-0.399520\pi$
$787$	−10.0308	−	5.79128i	−0.357559	−	0.206437i	−0.668009	+	0.744153i	$0.732853\pi$
$788$	5.66668	+	6.75328i	0.201867	+	0.240576i
$789$	−0.790836	−	32.6244i	−0.0281545	−	1.16146i
$790$	6.23602	−	10.8011i	0.221867	−	0.384286i
$791$	33.5820	+	58.1657i	1.19404	+	2.06813i
$792$	11.3315	+	1.43608i	0.402647	+	0.0510288i
$793$	34.6713	+	6.11348i	1.23121	+	0.217096i
$794$	3.99120	+	22.6352i	0.141643	+	0.803295i
$795$	−2.34153	+	6.95315i	−0.0830456	+	0.246603i
$796$	17.4686	+	14.6579i	0.619156	+	0.519534i
$797$	−51.1832			−1.81300			−0.906501	−	0.422204i	$-0.861256\pi$
$797$	−51.1832			−1.81300			−0.906501	+	0.422204i	$0.861256\pi$
$798$	20.2158	−	15.3733i	0.715632	−	0.544210i
$799$	7.12216			0.251964
$800$	−0.766044	−	0.642788i	−0.0270838	−	0.0227260i
$801$	−18.6019	−	28.8897i	−0.657265	−	1.02077i
$802$	−2.44263	−	13.8529i	−0.0862523	−	0.489161i
$803$	12.1986	+	2.15094i	0.430479	+	0.0759050i
$804$	12.3505	−	7.53544i	0.435570	−	0.265754i
$805$	−5.20766	−	9.01993i	−0.183546	−	0.317911i
$806$	−3.53115	+	6.11614i	−0.124380	+	0.215432i
$807$	−12.3305	+	0.298899i	−0.434054	+	0.0105217i
$808$	−3.70680	−	4.41759i	−0.130405	−	0.155410i
$809$	12.9654	+	7.48556i	0.455838	+	0.263178i	0.710293	−	0.703906i	$-0.248563\pi$
$809$	12.9654	+	7.48556i	0.455838	+	0.263178i	−0.254455	+	0.967085i	$0.581896\pi$
$810$	−5.09061	+	7.42198i	−0.178866	+	0.260782i
$811$	9.14236	−	25.1184i	0.321032	−	0.882027i	−0.669261	−	0.743028i	$-0.733389\pi$
$811$	9.14236	−	25.1184i	0.321032	−	0.882027i	0.990292	−	0.139000i	$-0.0443887\pi$
$812$	4.55617	−	25.8393i	0.159890	−	0.906782i
$813$	−4.18743	+	7.67666i	−0.146860	+	0.269232i
$814$	−34.9833	+	12.7329i	−1.22616	+	0.446287i
$815$	13.1511	−	15.6729i	0.460662	−	0.548996i
$816$	1.99560	−	2.49883i	0.0698601	−	0.0874765i
$817$	−12.0003	+	17.6997i	−0.419838	+	0.619234i
$818$			29.7400i			1.03983i
$819$	−32.8993	−	16.9245i	−1.14960	−	0.591390i
$820$	−2.15884	−	5.93136i	−0.0753899	−	0.207132i
$821$	2.03127	−	0.358167i	0.0708917	−	0.0125001i	−0.138090	−	0.990420i	$-0.544096\pi$
$821$	2.03127	−	0.358167i	0.0708917	−	0.0125001i	0.208982	+	0.977920i	$0.432985\pi$
$822$	−1.82430	−	2.07009i	−0.0636298	−	0.0722028i
$823$	9.37523	+	3.41231i	0.326800	+	0.118946i	0.500210	−	0.865904i	$-0.333256\pi$
$823$	9.37523	+	3.41231i	0.326800	+	0.118946i	−0.173410	+	0.984850i	$0.555478\pi$
$824$	−14.7565	+	8.51970i	−0.514069	+	0.296798i
$825$	2.40498	+	6.14039i	0.0837308	+	0.213781i
$826$	6.68176	−	5.60666i	0.232488	−	0.195081i
$827$	32.7123	−	27.4489i	1.13752	−	0.954491i	0.138163	−	0.990409i	$-0.455880\pi$
$827$	32.7123	−	27.4489i	1.13752	−	0.954491i	0.999355	+	0.0359183i	$0.0114356\pi$
$828$	−2.75021	+	8.87201i	−0.0955764	+	0.308324i
$829$	30.7909	−	17.7771i	1.06941	−	0.617425i	0.141390	−	0.989954i	$-0.454843\pi$
$829$	30.7909	−	17.7771i	1.06941	−	0.617425i	0.928020	+	0.372529i	$0.121509\pi$
$830$	−5.67138	−	2.06421i	−0.196856	−	0.0716499i
$831$	−39.0164	+	34.3838i	−1.35346	+	1.19276i
$832$	−3.61038	+	0.636607i	−0.125167	+	0.0220704i
$833$	2.72551	+	7.48829i	0.0944334	+	0.259454i
$834$	−3.02058	−	14.9958i	−0.104594	−	0.519261i
$835$		−	18.0227i		−	0.623703i
$836$	−11.5571	+	11.9105i	−0.399709	+	0.411934i
$837$	9.00946	+	4.36197i	0.311412	+	0.150772i
$838$	16.9258	−	20.1714i	0.584692	−	0.696809i
$839$	20.7445	−	7.55037i	0.716179	−	0.260668i	0.0418762	−	0.999123i	$-0.486666\pi$
$839$	20.7445	−	7.55037i	0.716179	−	0.260668i	0.674303	+	0.738455i	$0.264444\pi$
$840$	−5.11503	−	2.79012i	−0.176485	−	0.0962684i
$841$	5.52829	−	31.3525i	0.190631	−	1.08112i
$842$	−5.47826	+	15.0514i	−0.188793	+	0.518705i
$843$	−5.89129	+	38.9020i	−0.202907	+	1.33986i
$844$	18.5708	+	10.7219i	0.639234	+	0.369062i
$845$	−0.282881	−	0.337124i	−0.00973140	−	0.0115974i
$846$	−7.00040	+	9.21508i	−0.240679	+	0.316821i
$847$	5.88036	−	10.1851i	0.202051	−	0.349963i
$848$	2.11796	+	3.66841i	0.0727310	+	0.125974i
$849$	−7.09512	−	11.6289i	−0.243504	−	0.399102i
$850$	1.81826	+	0.320608i	0.0623658	+	0.0109968i
$851$	−5.25706	−	29.8143i	−0.180210	−	1.02202i
$852$	20.6205	+	6.94414i	0.706448	+	0.237902i
$853$	−1.05579	−	0.885910i	−0.0361494	−	0.0303330i	0.624534	−	0.780998i	$-0.285289\pi$
$853$	−1.05579	−	0.885910i	−0.0361494	−	0.0303330i	−0.660683	+	0.750665i	$0.729733\pi$
$854$	32.3047			1.10544
$855$	−4.17962	−	12.3908i	−0.142940	−	0.423755i
$856$	−12.5777			−0.429897
$857$	−37.3412	−	31.3330i	−1.27555	−	1.07031i	−0.993841	−	0.110814i	$-0.964654\pi$
$857$	−37.3412	−	31.3330i	−1.27555	−	1.07031i	−0.281709	−	0.959500i	$-0.590901\pi$
$858$	22.9119	+	7.71577i	0.782198	+	0.263412i
$859$	−6.80614	−	38.5995i	−0.232222	−	1.31700i	−0.848385	−	0.529380i	$-0.822425\pi$
$859$	−6.80614	−	38.5995i	−0.232222	−	1.31700i	0.616163	−	0.787619i	$-0.288686\pi$
$860$	4.83136	+	0.851898i	0.164748	+	0.0290495i
$861$	−19.1550	−	31.3950i	−0.652801	−	1.06994i
$862$	6.09431	+	10.5556i	0.207573	+	0.359527i
$863$	−10.7920	+	18.6923i	−0.367364	+	0.636293i	−0.989152	−	0.146892i	$-0.953073\pi$
$863$	−10.7920	+	18.6923i	−0.367364	+	0.636293i	0.621789	+	0.783185i	$0.286406\pi$
$864$	1.27165	+	5.03814i	0.0432624	+	0.171401i
$865$	0.432992	+	0.516019i	0.0147222	+	0.0175452i
$866$	−18.3210	−	10.5776i	−0.622572	−	0.359442i
$867$	3.52477	−	23.2752i	0.119707	−	0.790466i
$868$	−2.21639	+	6.08948i	−0.0752291	+	0.206690i
$869$	−8.24581	+	46.7643i	−0.279720	+	1.58637i
$870$	−11.8599	−	6.46928i	−0.402088	−	0.219329i
$871$	28.7760	−	10.4736i	0.975037	−	0.354884i
$872$	−5.64321	+	6.72532i	−0.191103	+	0.227748i
$873$	2.84390	−	0.644930i	0.0962515	−	0.0218276i
$874$	−7.90653	−	10.9373i	−0.267442	−	0.369961i
$875$		−	3.36394i		−	0.113722i
$876$	1.11270	+	5.52403i	0.0375946	+	0.186640i
$877$	5.50850	+	15.1345i	0.186009	+	0.511055i	0.997288	−	0.0736044i	$-0.0234502\pi$
$877$	5.50850	+	15.1345i	0.186009	+	0.511055i	−0.811279	+	0.584660i	$0.801228\pi$
$878$	19.0474	−	3.35857i	0.642818	−	0.113346i
$879$	−38.4839	+	33.9146i	−1.29803	+	1.14391i
$880$	3.57776	+	1.30220i	0.120606	+	0.0438971i
$881$	25.1508	−	14.5208i	0.847352	−	0.489219i	−0.0124046	−	0.999923i	$-0.503949\pi$
$881$	25.1508	−	14.5208i	0.847352	−	0.489219i	0.859756	+	0.510704i	$0.170615\pi$
$882$	−12.3677	−	3.83384i	−0.416443	−	0.129092i
$883$	1.36263	−	1.14338i	0.0458563	−	0.0384780i	−0.619572	−	0.784940i	$-0.712694\pi$
$883$	1.36263	−	1.14338i	0.0458563	−	0.0384780i	0.665428	+	0.746462i	$0.268249\pi$
$884$	5.18513	−	4.35084i	0.174395	−	0.146335i
$885$	−1.63785	−	4.18175i	−0.0550558	−	0.140568i
$886$	14.5646	−	8.40886i	0.489306	−	0.282501i
$887$	38.0176	+	13.8373i	1.27651	+	0.464610i	0.889275	−	0.457373i	$-0.151209\pi$
$887$	38.0176	+	13.8373i	1.27651	+	0.464610i	0.387231	+	0.921983i	$0.373432\pi$
$888$	−11.1974	−	12.7061i	−0.375761	−	0.426387i
$889$	−42.0761	+	7.41916i	−1.41119	+	0.248831i
$890$	−3.91732	−	10.7628i	−0.131309	−	0.360769i
$891$	8.54809	−	33.1831i	0.286372	−	1.11167i
$892$		−	9.21184i		−	0.308435i
$893$	−4.59602	−	16.1742i	−0.153800	−	0.541248i
$894$	13.3804	−	16.7546i	0.447509	−	0.560356i
$895$	11.8399	−	14.1103i	0.395765	−	0.471655i
$896$	−3.16107	+	1.15054i	−0.105604	+	0.0384367i
$897$	−9.41456	+	17.2594i	−0.314343	+	0.576273i
$898$	0.242943	−	1.37780i	0.00810711	−	0.0459777i
$899$	−5.13899	+	14.1193i	−0.171395	+	0.470904i
$900$	−2.20200	+	2.03745i	−0.0734000	+	0.0679150i
$901$	−6.77303	−	3.91041i	−0.225642	−	0.130275i
$902$	15.4476	+	18.4098i	0.514350	+	0.612978i
$903$	28.5759	−	0.692696i	0.950945	−	0.0230515i
$904$	9.98292	−	17.2909i	0.332027	−	0.575088i
$905$	−11.0897	−	19.2080i	−0.368635	−	0.638494i
$906$	11.4076	−	6.96010i	0.378991	−	0.231234i
$907$	29.8452	+	5.26251i	0.990993	+	0.174739i	0.645564	−	0.763706i	$-0.276622\pi$
$907$	29.8452	+	5.26251i	0.990993	+	0.174739i	0.345429	+	0.938445i	$0.387733\pi$
$908$	−0.624104	−	3.53947i	−0.0207116	−	0.117461i
$909$	−14.5458	+	9.36592i	−0.482453	+	0.310648i
$910$	−9.44721	−	7.92715i	−0.313172	−	0.262782i
$911$	17.6396			0.584426			0.292213	−	0.956353i	$-0.405608\pi$
$911$	17.6396			0.584426			0.292213	+	0.956353i	$0.405608\pi$
$912$	−6.96254	−	2.91942i	−0.230553	−	0.0966715i
$913$	22.9789			0.760490
$914$	5.62090	+	4.71649i	0.185923	+	0.156008i
$915$	5.30848	−	15.7635i	0.175493	−	0.521124i
$916$	1.85065	+	10.4956i	0.0611472	+	0.346783i
$917$	−7.47053	−	1.31726i	−0.246699	−	0.0434996i
$918$	−6.68429	−	6.88182i	−0.220615	−	0.227134i
$919$	−28.7956	−	49.8754i	−0.949879	−	1.64524i	−0.745675	−	0.666310i	$-0.767873\pi$
$919$	−28.7956	−	49.8754i	−0.949879	−	1.64524i	−0.204204	−	0.978928i	$-0.565460\pi$
$920$	−1.54808	+	2.68136i	−0.0510388	+	0.0884017i
$921$	0.803920	+	33.1642i	0.0264901	+	1.09280i
$922$	−21.7583	−	25.9305i	−0.716570	−	0.853975i
$923$	39.8839	+	23.0270i	1.31280	+	0.757943i
$924$	21.9337	+	3.32161i	0.721564	+	0.109273i
$925$	3.34426	−	9.18828i	0.109959	−	0.302109i
$926$	4.34118	−	24.6200i	0.142660	−	0.809065i
$927$	19.7904	+	47.1318i	0.650001	+	1.54801i
$928$	−7.32937	+	2.66767i	−0.240598	+	0.0875706i
$929$	−36.3745	+	43.3494i	−1.19341	+	1.42225i	−0.311876	+	0.950123i	$0.600957\pi$
$929$	−36.3745	+	43.3494i	−1.19341	+	1.42225i	−0.881531	+	0.472125i	$0.843487\pi$
$930$	2.60722	+	2.08217i	0.0854941	+	0.0682769i
$931$	15.2468	−	11.0218i	0.499695	−	0.361226i
$932$			23.6133i			0.773478i
$933$	−38.0961	+	7.67364i	−1.24721	+	0.251224i
$934$	3.50043	+	9.61736i	0.114538	+	0.314690i
$935$	−6.92280	+	1.22068i	−0.226400	+	0.0399204i
$936$	0.532893	+	10.9853i	0.0174182	+	0.359066i
$937$	−35.2439	−	12.8277i	−1.15137	−	0.419064i	−0.305362	−	0.952236i	$-0.598777\pi$
$937$	−35.2439	−	12.8277i	−1.15137	−	0.419064i	−0.846007	+	0.533172i	$0.821000\pi$
$938$	24.3345	−	14.0495i	0.794550	−	0.458734i
$939$	13.5034	−	5.28882i	0.440666	−	0.172594i
$940$	−2.95502	+	2.47956i	−0.0963822	+	0.0808743i
$941$	−19.4946	+	16.3579i	−0.635505	+	0.533252i	−0.902634	−	0.430409i	$-0.858369\pi$
$941$	−19.4946	+	16.3579i	−0.635505	+	0.533252i	0.267129	+	0.963661i	$0.413925\pi$
$942$	11.8552	−	4.64329i	0.386264	−	0.151286i
$943$	−16.9248	+	9.77153i	−0.551147	+	0.318205i
$944$	−2.43654	−	0.886829i	−0.0793027	−	0.0288638i
$945$	−10.2333	+	14.1709i	−0.332888	+	0.460981i
$946$	−18.3948	+	3.24350i	−0.598066	+	0.105455i
$947$	−8.43237	−	23.1678i	−0.274015	−	0.752851i	−0.998011	−	0.0630459i	$-0.979919\pi$
$947$	−8.43237	−	23.1678i	−0.274015	−	0.752851i	0.723995	−	0.689805i	$-0.242304\pi$
$948$	−21.1769	+	4.26562i	−0.687792	+	0.138541i
$949$			11.9271i			0.387168i
$950$	−0.445258	−	4.33610i	−0.0144461	−	0.140682i
$951$	42.1077	+	33.6278i	1.36544	+	1.09046i
$952$	3.99228	−	4.75781i	0.129390	−	0.154201i
$953$	27.9455	−	10.1713i	0.905244	−	0.329482i	0.152892	−	0.988243i	$-0.451141\pi$
$953$	27.9455	−	10.1713i	0.905244	−	0.329482i	0.752352	+	0.658761i	$0.228919\pi$
$954$	11.7168	−	4.91980i	0.379344	−	0.159284i
$955$	−3.25577	+	18.4644i	−0.105354	+	0.597493i
$956$	−6.21322	+	17.0707i	−0.200950	+	0.552105i
$957$	50.8561	+	7.70161i	1.64395	+	0.248958i
$958$	2.21831	+	1.28074i	0.0716703	+	0.0413789i
$959$	−3.44464	−	4.10516i	−0.111233	−	0.132562i
$960$	0.0419736	+	1.73154i	0.00135469	+	0.0558853i
$961$	−13.6445	+	23.6330i	−0.440145	+	0.762354i
$962$	−17.9234	−	31.0442i	−0.577873	−	1.00090i
$963$	−4.74410	+	37.4337i	−0.152876	+	1.20628i
$964$	−24.0801	−	4.24597i	−0.775567	−	0.136753i
$965$	0.152915	+	0.867227i	0.00492252	+	0.0279170i
$966$	−5.75738	+	17.0965i	−0.185241	+	0.550070i
$967$	24.0148	+	20.1508i	0.772263	+	0.648005i	0.941287	−	0.337607i	$-0.109617\pi$
$967$	24.0148	+	20.1508i	0.772263	+	0.648005i	−0.169025	+	0.985612i	$0.554062\pi$
$968$	−3.49611			−0.112369
$969$	13.8278	−	1.75950i	0.444214	−	0.0565234i
$970$	0.972037			0.0312102
$971$	−2.27167	−	1.90615i	−0.0729013	−	0.0611714i	0.605609	−	0.795762i	$-0.292930\pi$
$971$	−2.27167	−	1.90615i	−0.0729013	−	0.0611714i	−0.678510	+	0.734591i	$0.737374\pi$
$972$	15.4741	−	1.88438i	0.496333	−	0.0604414i
$973$	−5.15897	−	29.2580i	−0.165389	−	0.937968i
$974$	−25.1233	−	4.42992i	−0.805003	−	0.141944i
$975$	−5.42055	+	3.30724i	−0.173597	+	0.105917i
$976$	−4.80162	−	8.31665i	−0.153696	−	0.266209i
$977$	10.9092	−	18.8952i	0.349015	−	0.604512i	−0.637060	−	0.770814i	$-0.719850\pi$
$977$	10.9092	−	18.8952i	0.349015	−	0.604512i	0.986075	+	0.166303i	$0.0531829\pi$
$978$	−35.4264	+	0.858757i	−1.13281	+	0.0274600i
$979$	28.0305	+	33.4055i	0.895859	+	1.06764i
$980$	−3.73786	−	2.15805i	−0.119401	−	0.0689365i
$981$	17.8873	+	19.3320i	0.571098	+	0.617222i
$982$	−7.56578	+	20.7868i	−0.241434	+	0.663333i
$983$	−8.03251	+	45.5546i	−0.256197	+	1.45297i	0.536783	+	0.843720i	$0.319639\pi$
$983$	−8.03251	+	45.5546i	−0.256197	+	1.45297i	−0.792980	+	0.609247i	$0.791472\pi$
$984$	−5.23532	+	9.59772i	−0.166896	+	0.305964i
$985$	8.28413	−	3.01518i	0.263954	−	0.0960715i
$986$	9.25663	−	11.0316i	0.294791	−	0.351318i
$987$	−14.0257	+	17.5625i	−0.446443	+	0.559022i
$988$	−13.2266	−	8.96759i	−0.420795	−	0.285297i
$989$		−	15.1894i		−	0.482996i
$990$	5.22507	−	10.1570i	0.166064	−	0.322809i
$991$	8.26147	+	22.6982i	0.262434	+	0.721033i	0.999002	+	0.0446685i	$0.0142232\pi$
$991$	8.26147	+	22.6982i	0.262434	+	0.721033i	−0.736567	+	0.676364i	$0.763555\pi$
$992$	1.89713	−	0.334515i	0.0602339	−	0.0106209i
$993$	−39.4704	−	44.7883i	−1.25256	−	1.42131i
$994$	39.7101	+	14.4533i	1.25953	+	0.458430i
$995$	19.7485	−	11.4018i	0.626069	−	0.361461i
$996$	3.81232	+	9.73359i	0.120798	+	0.308421i
$997$	14.7301	−	12.3600i	0.466506	−	0.391445i	−0.379012	−	0.925392i	$-0.623736\pi$
$997$	14.7301	−	12.3600i	0.466506	−	0.391445i	0.845518	+	0.533947i	$0.179292\pi$
$998$	−7.47324	+	6.27079i	−0.236561	+	0.198498i
$999$	−42.0392	+	28.5332i	−1.33006	+	0.902749i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bb.a.41.3	✓	84
3.2	odd	2		570.2.bb.b.41.9	yes	84
19.13	odd	18		570.2.bb.b.431.9	yes	84
57.32	even	18	inner	570.2.bb.a.431.3	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.41.3	✓	84	1.1	even	1	trivial
570.2.bb.a.431.3	yes	84	57.32	even	18	inner
570.2.bb.b.41.9	yes	84	3.2	odd	2
570.2.bb.b.431.9	yes	84	19.13	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(-1.64147 - 0.552780i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(-0.902121 - 1.47857i) q^{6} +(-1.68197 - 2.91326i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.38887 + 1.81475i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(-1.64147 - 0.552780i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(-0.902121 - 1.47857i) q^{6} +(-1.68197 - 2.91326i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.38887 + 1.81475i) q^{9} +(0.642788 + 0.766044i) q^{10} +(-3.29728 - 1.90369i) q^{11} +(0.259343 - 1.71252i) q^{12} +(1.25387 - 3.44498i) q^{13} +(0.584142 - 3.31284i) q^{14} +(-1.52055 - 0.829421i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.18678 - 1.41436i) q^{17} +(0.663483 + 2.92571i) q^{18} +(-3.97780 - 1.78244i) q^{19} +1.00000i q^{20} +(1.15052 + 5.71180i) q^{21} +(-1.30220 - 3.57776i) q^{22} +(3.04913 - 0.537643i) q^{23} +(1.29946 - 1.14517i) q^{24} +(0.939693 + 0.342020i) q^{25} +(3.17491 - 1.83304i) q^{26} +(-2.91811 - 4.29938i) q^{27} +(2.57693 - 2.16230i) q^{28} +(5.97496 - 5.01358i) q^{29} +(-0.631665 - 1.61276i) q^{30} +(-1.66831 + 0.963198i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(4.36008 + 4.94753i) q^{33} +(1.81826 - 0.320608i) q^{34} +(-1.15054 - 3.16107i) q^{35} +(-1.37235 + 2.66770i) q^{36} -9.77797i q^{37} +(-1.90144 - 3.92231i) q^{38} +(-3.96251 + 4.96173i) q^{39} +(-0.642788 + 0.766044i) q^{40} +(-5.93136 + 2.15884i) q^{41} +(-2.79012 + 5.11503i) q^{42} +(0.851898 - 4.83136i) q^{43} +(1.30220 - 3.57776i) q^{44} +(2.03745 + 2.20200i) q^{45} +(2.68136 + 1.54808i) q^{46} +(2.47956 + 2.95502i) q^{47} +(1.73154 - 0.0419736i) q^{48} +(-2.15805 + 3.73786i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-2.72990 + 1.66560i) q^{51} +(3.61038 + 0.636607i) q^{52} +(-0.735560 - 4.17157i) q^{53} +(0.528186 - 5.16924i) q^{54} +(-2.91662 - 2.44733i) q^{55} +3.36394 q^{56} +(5.54415 + 5.12468i) q^{57} +7.79975 q^{58} +(1.98629 + 1.66669i) q^{59} +(0.552780 - 1.64147i) q^{60} +(1.66758 + 9.45734i) q^{61} +(-1.89713 - 0.334515i) q^{62} +(1.26882 - 10.0117i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.83304 - 3.17491i) q^{65} +(0.159809 + 6.59263i) q^{66} +(5.36922 + 6.39878i) q^{67} +(1.59895 + 0.923155i) q^{68} +(-5.30226 - 0.802969i) q^{69} +(1.15054 - 3.16107i) q^{70} +(-2.18141 + 12.3714i) q^{71} +(-2.76605 + 1.16145i) q^{72} +(-3.05716 + 1.11271i) q^{73} +(6.28516 - 7.49036i) q^{74} +(-1.35342 - 1.08086i) q^{75} +(1.06463 - 4.22689i) q^{76} +12.8078i q^{77} +(-6.22480 + 1.25385i) q^{78} +(-4.26569 - 11.7199i) q^{79} +(-0.984808 + 0.173648i) q^{80} +(2.41339 + 8.67038i) q^{81} +(-5.93136 - 2.15884i) q^{82} +(-5.22677 + 3.01768i) q^{83} +(-5.42524 + 2.12488i) q^{84} +(1.41436 - 1.18678i) q^{85} +(3.75813 - 3.15344i) q^{86} +(-12.5791 + 4.92683i) q^{87} +(3.29728 - 1.90369i) q^{88} +(-10.7628 - 3.91732i) q^{89} +(0.145358 + 2.99648i) q^{90} +(-12.1451 + 2.14151i) q^{91} +(1.05895 + 2.90944i) q^{92} +(3.27092 - 0.658857i) q^{93} +3.85751i q^{94} +(-3.60785 - 2.44610i) q^{95} +(1.35342 + 1.08086i) q^{96} +(0.624814 - 0.744624i) q^{97} +(-4.05581 + 1.47620i) q^{98} +(-4.42207 - 10.5314i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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